Problem is, you would have many weak skills, actually too much of them that you wouldn’t use all.
You could choose 2-3 main classes and invest into them, using the first ranks for buffs only.
Also keep in mind Cannonner and SR don’t go along that well. Sure you can dismount and mount again (cannonner skills cannot be used while mounted) but Cann skills have so low CD that it wouldn’t feel fluid. I would recommend either choosing classes which can be useful while mounted or giving up on SR.
Maybe something like:
Archer -> Archer -> Sapper -> Sapper -> ? -> ? -> Cannonner
So you get crit bonus from archer + sapper traps + cannonner while traps do their work. Ranger buff does not affect sapper skills, but do affect Cannonner. Wugushi C2 could maybe be a fill option here, although poison do not benefit from archer bonus.
Another option:
Archer -> Archer -> Sapper -> Sapper -> Fletcher -> SR -> SR
This way you lay down ur traps and mount to use SR skills while traps do their work. Archer buff can be used both mounted and unmounted. Fletcher is there to fill your cooldown time, and fletcher skills can be used while mounted. Problem is SR 2 is apparently lackluster.