Where do our spirits go between incarnations and densities?

[anagogy]

What is the purpose of multiple incarnations in 4th density then? If there is no veil of forgetfulness in 4th density, so that entity can progress freely and works towards its goal of further ultimate polarization. Why "die" and reincarnate?

For much the same reason that we reincarnate in 3rd density. To experience life in different bodies. It gives one a different nuance of experience. A slightly different vantage point. Beyond 4th density, you can more or less manifest and demanifest the physical form at will though, so I guess you could think of those as rapid incarnations.