Migrated Content

Quick answer is no.
There are things like symbols and patterns that you can place in multiple layers… when you edit the pattern or symbol all "instances" referencing it are uppdated.
Using the appearance a vector can have several fills or outlines… in one way we can say it is a path with many layers. But a path can only be in one layer, that is also true for a group. (this is true for most applications)
If you explain more why you want to draw on several layers it may be easier to come with the best solution for you.