John 14:2-3 In my Father's house are many mansions

² In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you. ³ And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also. John 14:2-3 Bible, King James Version

That there are in fact many Planes in the Spirit World is I believe taught symbolically by Jesus in the Bible where He says: In my Father’s House are many Mansions. (John 14:2) Also in the Bible (Luke 16:19-31) Jesus tells the story of Lazarus and the Rich man. Lazarus is a beggar, full of sores, begging at the gate of a rich man. Lazarus dies and is carried by the angels into Abraham’s bosom, or Paradise, and the rich man dies and goes to hell. From hell the rich man cries out to Abraham for help but he is unable to help him. Abraham points out that between them there is a great gulf fixed. Realizing the predicament he has got himself into the rich man is then concerned for his family back on earth so they don’t end up in hell also. He asks if one from the dead could be sent to warn them. Abraham points out that even if one rose from the dead they still wouldn’t be persuaded. There are a series of Higher and lower Planes. For most people these represent great gulfs which they cannot easily cross because of their varying states of consciousness or higher and lower frequencies.

Concerning the divisions between the heavens Emanuel Swedenborg teaches: Chapter 5 vs. 29. There are three heavens, entirely distinct from each other, an inmost or third, a middle or second, and an outmost or first… 34. …Because in the angels of the inmost heaven the interiors have been opened in the third degree their perfection immeasurably surpasses the perfection of angels in the middle heaven, whose interiors have been opened in the second degree. So the perfection of these angels exceeds in like measure the perfection of angels of the outmost heaven. 35. Because of this distinction an angel of one heaven cannot go among the angels of another heaven, that is, no one can ascend from a lower heaven and no one can descend from a higher heaven… There were some from the outmost heaven who had not yet been taught that the interiors of angels are what constitute heaven, and who believed that they might come into a higher heavenly happiness by simply gaining access to a heaven where higher angels are. These were permitted to enter among such angels. But when they were there they could see no one, however much they searched, although there was a great multitude present; for the interiors of the newcomers not having been opened in the same degree as the interiors of the angels there, their sight was not so opened… Therefore they hastily betook themselves to the heaven from which they came, glad to get back among their like, and pledging themselves that they would no longer covet higher things than were in agreement with their life… It is otherwise when, as is often done, angels are raised up by the Lord out of a lower heaven into a higher that they may behold its glory; for then they are prepared beforehand, and are encompassed by intermediate angels, through whom they have communication with those they come among. From all this it is plain that the three heavens are entirely distinct from each other. Footnotes to Chapter 14: …The hells are at a distance from the heavens because they cannot bear the presence of Divine love from the Lord. For this reason the hells are very far away from the heavens, and this is the “great gulf.” (Heaven and its Wonders and Hell From Things Heard and Seen by Emanuel Swedenborg)

It is however possible to cross these great gulfs so long as we are taught how, which means that no one needs to stay in hell or a lower Plane. Everyone eventually spiritually progresses up from the lower Planes to the higher Planes.

Come Together by  h.koppdelaney

These huge gulfs are symbolized by seeing a Sun, Moon, Star or Planet in the inner sky which creates the illusion of there being a huge gulf or distance between you and the higher World or higher Plane. Within the individual Planes I believe the angels, or more spiritually advanced spirits, dwell on higher ground symbolizing a higher Plane while less spiritually advanced spirits dwell on the lower ground, symbolizing the lower Planes. On this subject Emanuel Swedenborg teaches: Chapter 21 vs. 188. The angels of whom the Lord’s celestial kingdom consists dwell for the most part in elevated places that appear as mountains… the angels of whom the Lord’s spiritual kingdom consists dwell in less elevated places that appear like hills; while the angels in the lowest parts of heaven dwell in places that appear like ledges of stone. These things spring from correspondence, for interior things correspond to higher things, and exterior things to lower things. (Heaven and its Wonders and Hell From Things Heard and Seen by Emanuel Swedenborg) Therefore a basic rule is; travelling upwards leads towards Heaven, travelling downwards leads towards hell.

"In my Father's house are many mansions" can also be taken literally: 

Heaven and Hell, by Emanuel Swedenborg, [1758], tr. by John C. Ager [1900] at sacred-texts.com

183.
THE PLACES OF ABODE AND DWELLINGS OF ANGELS. As there are societies in heaven and the angels live as men, they have also places of abode, and these differ in accordance with each one's state of life. They are magnificent for those in higher dignity, and less magnificent for those in lower condition. I have frequently talked with angels about the places of abode in heaven, saying that scarcely any one will believe at the present day that they have places of abode and dwellings; some because they do not see them, some because they do not know that angels are men, and some because they believe that the angelic heaven is the heaven that they see with their eyes around them, and as this appears empty and they suppose that angels are ethereal forms, they conclude that they live in ether. Moreover, they do not comprehend how there can be such things in the spiritual world as there are in the natural world, because they know nothing about the spiritual. [2] The angels replied that they are aware that such ignorance prevails at this day in the world, and to their astonishment, chiefly within the church, and more with the intelligent than with those whom they call simple. They said also that it might be known from the Word that angels are men, since those that have been seen have been seen as men; and the Lord, who took all His Human with Him, appeared in like manner. It might be known also that as angels are men they have dwellings and places of abode, and do not fly about in air, as some think in their ignorance, which the angels call insanity, and that although they are called spirits they are not winds. This they said might be apprehended if men would only think independently of their acquired notions about angels and spirits... For everyone has a general idea that angels are in the human form, and have homes which are called the mansions of heaven, which surpass in magnificence earthly dwellings; but this general idea, which flows in from heaven, at once falls to nothing when it is brought under direct scrutiny and inquiry whether it is so, as happens especially with the learned, who by their own intelligence have closed up heaven to themselves and the entrance of heavenly light. [3] The like is true of the belief in the life of man after death. When one speaks of it, not thinking at the same time about the soul from the light of worldly learning or from the doctrine of its reunion with the body, he believes that after death he is to live a man, and among angels if he has lived well, and that he will then see magnificent things and perceive joys; but as soon as he turns his thoughts to the doctrine of reunion with the body, or to his theory about the soul, and the question arises whether the soul be such, and thus whether this can be true, his former idea is dissipated.
184.
But it is better to present the evidence of experience. Whenever I have talked with angels face to face, I have been with them in their abodes. These abodes are precisely like abodes on the earth which we call houses, but more beautiful. In them there are chambers, parlors, and bedrooms in great number; there are also courts, and there are gardens and flower beds and lawns round about. Where they live together their houses are near each other, arranged one next to the other in the form of a city, with avenues, streets, and public squares, exactly like cities on the earth. I have been permitted to pass through them, looking about on every side, and sometimes entering the houses. This occurred when my inner sight was opened, and I was fully awake. [184-1 Angels have cities, palaces and houses (n. 940-942, 1116, 1626-1631, 4622).] 
185.
I have seen palaces in heaven of such magnificence as cannot be described. Above they glittered as if made of pure gold, and below as if made of precious stones, some more splendid than others. It was the same within. Both words and knowledge are inadequate to describe the decorations that adorned the rooms. On the side looking to the south there were parks, where, too, everything shone, in some places the leaves glistening as if made of silver, and fruit as if made of gold; while the flowers in their beds formed rainbows with their colors. Beyond the borders, where the view terminated, were seen other palaces. Such is the architecture of heaven that... the art itself is from heaven. The angels said that such things and innumerable others still more perfect are presented before their eyes by the Lord; and yet these things are more pleasing to their minds than to their eyes, because in everyone of them they see a correspondence, and through the correspondences what is Divine.
186.
As to these correspondences I have also been told that not only the palaces and houses, but all things and each thing, both inside and outside of them, correspond to the interior things which they have from the Lord, the house itself in general corresponding to their good, the particular things inside of a house to the various things of which their good consists, [186-1 "Houses," with their contents, signify the things in man that belong to his mind, thus his interiors (n. 710, 2233, 2331, 2559, 3128, 3538, 4973, 5023, 6639, 6690, 7353, 7848, 7910, 7929, 9150); consequently the things relating to good and truth (n. 2233, 2331, 2559, 4982, 7848, 7929). "Rooms" and "bed-chambers" signify interior things there (n. 3900, 5694, 7353). The "roof of a house" signifies what is inmost (n. 3652, 10184). A "house of wood" signifies what relates to good, and a "house of stone" what relates to truth (n. 3720).] and the things outside to truths derived from good, and also to their perceptions and knowledges  [186-2 A "garden" or "park" signifies intelligence and wisdom (n. 100, 108, 3220). What is meant by "the garden of Eden" and "the garden of Jehovah" (n. 99, 100, 1588). How magnificent the things seen in parks are in the other life (n. 1122, 1622, 2296, 4528, 4529). "Trees" signify perceptions and knowledges, from which wisdom and intelligence are derived (n. 103, 2163, 2682, 2722, 2972, 7692). "Fruits" signify goods of love and goods of charity (n. 3146, 7690, 9337).] and as these things correspond to the goods and truths they have from the Lord they correspond to their love, and to their wisdom and intelligence from love, since love belongs to good, wisdom to good and truth together, and intelligence to truth from good. These are what the angels perceive when they behold what is around them, and thus their minds are more delighted and moved by them than their eyes...
188.
The angels of whom the Lord's celestial kingdom consists dwell for the most part in elevated places that appear as mountains of soil; the angels of whom the Lord's spiritual kingdom consists dwell in less elevated places that appear like hills; while the angels in the lowest parts of heaven dwell in places that appear like ledges of stone. These things spring from correspondence, for interior things correspond to higher things, and exterior things to lower things; and this is why in the Word "mountains" signify celestial love, "hills" spiritual love, and "rocks" faith. [188-2 In the Word what is interior is expressed by what is higher and what is higher signifies what is interior (n. 2148, 3084, 4599, 5146, 8325). What is "high" signifies what is internal, and likewise heaven (n. 1735, 2148, 4210, 4599, 8153). In heaven, mountains, hills, rocks, valleys, and lands are seen exactly the same as in the world (n. 10608). On the mountains angels who are in the good of love dwell, on the hills those who are in the good of charity, on the rocks those who are in the good of faith (n. 10438). Therefore in the Word "mountains" signify the good of love (n. 795, 4210, 6435, 8327, 8758, 10438, 10608). "Hills" signify the good of charity (n. 6435, 10438). "Rocks" signify the good and truth of faith (n. 8581, 10580). "Stone," of which rock consists, in like manner signifies the truth of faith (n. 114, 643, 1298, 3720, 6426, 8609, 10376). This is why "mountains" signify heaven (n. 8327, 8805, 9420). And "the summit of a mountain" signifies the highest part of heaven (n. 9422, 9434, 10608). Also why the ancients had their holy worship on mountains (n. 796, 2722).]
189.
There are also angels who do not live associated together, but apart, house by house. These dwell in the midst of heaven, since they are the best of angels.
190.
The houses in which angels dwell are not erected, as houses in the world are, but are given to them gratuitously by the Lord, to everyone in accordance with his reception of good and truth. They also change a little in accordance with changes of the state of interiors of the angels (of which above, n. 154-160). Everything whatsoever that the angels possess they hold as received from the Lord; and everything they have need of is given them.