Lighting advice:Possible to have "reflected light" near an objects shadow with moveable light?

3dmax, even that old, probably have some raytracing GI solution.
In UE4 you can experiment with Skylight/direct light. There some settings which add some kind of reflected light from ground.

Im currently make some prove of concept for suck a task like roughly approimated dynamic GI:
https://youtu.be/2_gWqdZN0Wg

But probably for you it would be better to chose: static or dynamic. If you chose dynamic - try RTX, cause LPV are abandoned, and looks like VXGI are also obsolete.
In static lighting you have volumetric lightmaps. They static, but can give nice feel of indirect light.