You can stack cut a variety of different thickness but the most common is 1/8" or 1/4". This technique is particularly useful for fretwork cutting. You spend the same amount of cut time but instead of one item you end up with up to 8 duplicates.
The magic number isn't necessarily 8 but I would not recommend going beyond that as the chances for things to go wrong increases. Stack 8 layers each 1/8" thick and secure all the layers together. You could tack glue the layers in negative waste areas to keep them all together. If all the sizes are similar, you can run a line of tape along the edges to secure them. You could also use some double sided tape but with intricate fretwork, this method can be long and tedious and tricky to remove the tape without damaging the piece. You could use layers of wood less than 1/8" thick but at that point, the wood becomes very fragile and if the blade catches the piece on the upstroke of a cut and slams it onto the table (always a cringe moment), strong chance that something will break.
So why not 10 layers? Well, the thicker the stack of wood the greater the chance of angled cuts. I've cut many fretwork pieces out where the top layer looks perfect but once you separate the layers, the cuts become less and less accurate and can ruin the bottom few layers. Cutting at 1" or less is a rule that I follow but it can certainly be done on a thicker stack.
One of the other possible occurrences that spell almost certain doom is if the stack of wood shifts. This can happen if the layers are not secured well enough. You want all the layers to be perfectly rigid to each other or cut will not match on the top and bottom layers.