Is your console a H6er? A notorious problem with them is on that model there is a hex buffer ic the trigger lines pass through ;when it goes bad it causes issues with the fire button... Every model afterwards eliminated the need for the hex buffer.
I'm sure it could be done. But how. A lot of people say that the sound chip in the game would make it hard, but I personally don't see a reason you couldn't make a piggy back cart that could leach the pitfall carts sound chip (kind of like knuckles for genesis, is what i'm thinking about)
Of course, some willing home brewer could probably make the extra caves as a standalone cart, ax the sound, or put different sound in (personally, the music was what made pitfall 2 for me, but apparently a lot of people think it's not needed)
Anyhow, possible? sure, likely? not really.
Harmony cart does great emulation of the DPC chip... with added features (DPC+). What about the melody boards?
I like the idea of an add on cart. Kernal runs from the addon and bankswitches to the original. Perhaps other games could do this using a pluged in pitfall 2 cart just for its DPC chip.