So, can we go back and forth between heaven and earth?
There are records of people physically going to heaven. The first is Enoch in Gen. 5:18-24. The second is Elijah in 2 Kings 2:1-11. These are the two witnesses who will return to earth in Revelation 11, prophesy against the antichrist, be killed, and then will rise from the dead and be taken to heaven on the third day. With the exception of those taken in the rapture, nobody escapes the
And as it is appointed unto men once to die, but after this the judgment
fact of life in Heb. 9:27-28. So with God, it is possible to move between heaven and earth but it is clear that as far as living people is concerned it doesn't happen often and only happens for God's ultimate purposes.
There are also many accounts such as Daniel and John who describe heaven via angelic messenger, or a vision or other mental state. In a contemporary setting, there is the story of a little boy who was at death's door and had a view of Jesus and heaven and an older sibling that he never knew about who had died prematurely. So there is also a mental state or vision means of going back and forth and catching glimpses of heaven. This also, by all accounts, doesn't happen very often and again is done for God's purposes.
Finally, there are people who have been resurrected - sometimes after days in the case of Lazarus - and who come back and live life out on earth. We would believe that their soul went to the appropriate place in the meantime - either the paradise compartment of the grave in the case of Lazarus (since Christ hadn't died yet) or heaven after Christ's resurrection for a righteous soul, or the punishment side of the grave for every other soul. So a person's soul can make that transfer and come back if God allows the body to be resurrected.
Certainly, angels go back and forth all the time at the behest of God or on their own.
What I don't see is any biblical evidence of souls coming back like ghosts or anything like that. I think that once you are in heaven, you stay there unless God has a particular purpose in sending you back (like Enoch and Elijah who technically haven't yet died the first time) or a rare resurrection.
It is clear from Christ's description of the rich man and Lazarus (a different one) in Matthew 16:15-31, that the souls who had died without accepting God's plan of salvation were stuck and couldn't come back. Likewise, the righteous souls were stuck until Christ led captivity captive and took them to heaven (Eph. 4:8-10) - with the exception of those resurrected in either the Old or New Testaments.
According to the New Testament, the living souls have some sort of identifiable body as the rich man was able to identify the patriarchs, but the resurrected body itself won't be joined back till the rapture of the church for those who have died in a saved state or the great white throne judgment for the wicked dead. So if we were to be allowed to go back and forth, the exact means of that would be unknown. I personally think that once you make it to heaven, you are so glad to get there where everything is good and God is, that you simply have absolutely no desire to come back.
Once the rapture has happened, it is said that God will have work for us to do, so I believe that ultimately we will be able to move from place to place, much as Christ was able to appear in the midst of His disciples, and move around the road back from the tomb, and ascend to heaven after His resurrection. So I know that in the resurrected body - which Christ had at this time - it will be possible and done. I'm just not comfortable saying you get to move back and forth till post rapture, and even then, I suspect you won't want to go out very often even when it is possible.