Is it possible? And if so, is it possible without losing important information in the process?
Depends on what "important informations" are.
FBX would be first choice, but the version for MAX 6 won't import UV coordinates.
OBJ would be the second best choice. It's really only ment to save the model and mapping, but nothing else.
3ds ... I don't like it, but it does save some more stuff.
You might want to take a look at this. It could be the best way to get your model into max 6 wihout loosing anything.
However, I have yet to test the script myself, so I don't know how well it works, other than reading about it.
The interesting thing is, that it should even keep your modifier stack(!)
http://www.scriptspot.com/3ds-max/bff-2007