You can always ask, Bear.
Depends on the timing too. If he has a backlog of better paying work, he may just say "Nope, fixed price". No reason to take a loss. OTOH if he has dry-spells he may say "ask me in August" or whatever month. Or, he may agree to a discount.
But for piece-work, generally not. The larger the job, the more discount. Piece work just means he has more total overhead doing several jobs over several years and gets no economics of scale like he would if he did it all at once. But it might be good "filler work" between profitable stuff.
Basically, it depends on his schedule and mood and costs and other jobs. You don't know unless you ask.