I've jumped from my SG500 to BBW. Natural stones are usually slower than synths, so your resulting edge will be something between 500 and ˜4k, depending on how much time you spend on the BBW (and also how easy your steel sharpens - probably best to try this with simple carbon steels). To get a "pure" ˜4k BBW edge you need to spend quite some time on your BBW, and it would be more practical jumping to a 1-2-3k synth and finish on the BBW. It's a great stone for the final deburr.
But, there are no rules. Many people here like big jumps between synths. These days I go from SG500 to Gesshin 4k frequently. Try it and let us know how it works