My first Handi I bought was a .243 youth model with the youth stock.
It has since grown up and the receiver is the only thing that is still original from that first rifle.
The original receiver now wears a laminated thumbhole stock by Boyd's and a 45-70 barrel.
It also at times sports a 12 ga. Tracker 2 barrel, and once had a .223 barrel attached to it.
So the answer to your question is yes, just change out stocks, barrels, whatever.
Like Tim said, used barrels bought over the Classifieds section may, or may not fit, and then you would refer to the FAQ's at the top of the page.
I've bought a few barrels and so far I've been pretty lucky in that only two had to be shimmed in order to lock up tight.
Welcome to the addiction!