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There are some patterns that use a round disc to make items using 24 strands. Is there a bigger disc that allows for this? I have a disc that goes from 1 thru 32 [doing a strand on each side of the number. This then counts out for 16 total strands. Can someone show me how to do the patterns that require the use of 24 strands on a regular 32 count disc?

You always need twice as much slots as strings, so 16 strings require 32 slots, 40 strings require 80 slots. You could do with less, but then you'll always have two pairs of strings next to each other without a slot in between. That's difficult to work with.
You can make your own disc out of cardboard, if you like you can use the kumiwheel- generator.

kumiwheel generator