I steer people away from using the TL866ii+ with the adapter for the large EPROMs because you have to split each file you want to write into chunks and then write them to the EPROM one chunk at a time, incrementing the dial on the adapter with each chunk. It's slow and error-prone.
Better to just spend a little more upfront on a better programmer and save yourself the hassle - especially considering that most of the arcade Multis and Neo Geo carts you'd want to buy a programmer for use those large EPROMs.
The Sega System 16 Multi for example uses 15 27C322 EPROMs. Each 27C322 EPROM file has to be broken into 8 chunks with the TL866ii+. 15 * 8 = 120 individual chunks you have to write to program 15 EPROMs - you'll be there forever!