Nothing to do with sets etc, it's down to how the items were made. There's a hard limit on the number of segments for hair, so if you have 2 activated priority goes to the first one alphabetically (like all items in TB). If both are using the same segment numbers then hair #1 will display. If there are left over segments then depending on the client version you may end up with some pieces of hair #2 showing - which looks pretty crap TBH.
However you can do hair + a head 3D item as they're completely different things. Eg hair + shades.
Same limit applies to 3D objects however, only 1 per body piece.
Hope that explains the situation, and why there are a limited number of compilations of hair that work together due to non-overlapping segments being used. (search/google for info on which work and if it's only specific client versions allowing specific combos)
If people are wanting 2 styles to be made into a single piece then it may be worth prodding the forgers into making some dedicated combination items.