Depends on the pistons, camshaft profile, timing, etc... without the rest of the engine info no one can help you.
408 and it really cant handle that
Bore it .030 over. A 350 has a 4 inch bore. When you go .030 over, the cid., becomes 355.
4.030"
You can bore a 350 .090 over, but the thing is the bore is so big that the cylinder walls are about a hair line thickness apart. In order for the engine to accept the bore and punishment of the shear power, the 350 Block must be casted with extra carbon to strengthen the block.
4.060"
4.040"
355
it is a 30 over 350
Its not a matter of how little you can but how much, i would prolly say to be safe 70 or 80. If you bore to much out , the engine will run to hot, thus you need to be very careful and know what you are doing.
A 383 is a 350 block with a 400 crank. The block is bored to 4.030". A 400 has a 4.125" bore, so you'd need to bore the 383 roughly .095", which is probably not practical as the 350 is not made to be overbored that much.
The Banshee 350's horsepower is 40.5.
ive heard you can go 60 over (.060)