Welcome to the Reaper forums !
Of course in Reaper anything is possible
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There are lots of ways to do sound / patch handling in Reaper. Using multiple Midi channels might or might not make sense. I think limiting the count of possible patches to the 15 Midi remaining channels is not a good idea, you'd better use multiple tracks.
Please read the introductional thread in the "Live" subforum to find more information on patch handling.
Please come back in that forum if you need more help.
-Michael