Bump again. Any reason I can't join together sections of multiple chains to 1 new chain?

Sometimes I replace a rusty old chain with a new one. Because kids' bikes are so small, I get a lot of extra links left over from when I break the new chain. Couldn't I save up 3 or 4 sets of these extra leftover links and join them all together into one fresh new chain? I would make sure they're all of the same make and model of chain, and they would all be brand new to avoid mixing chains of different wear amounts.