| Nancy,
Do not take the backbulbs off. These backbulbs store energy for the rest of the plant and as they are alive and have leaves (active clorophyl) they continue to make energy for the plant. There's also no compelling reason to divide the plant so don't bother with that. More new growths mean more flowers when it blooms. It is very common for Cattleyas to "branch" in this way, putting out one new lead, then 2, then 4, then 6 or 7, etc., etc.
When you repot, don't put the new growth near the rim, doing so will make the next cycle of growth grow over the edge of the pot. Instead, position the plant with the backbulbs near the edge of the pot so that the new growths grow out into the pot. Choose a pot big enough to allow room for about 2 years' worth of new growth.
Let us know how the repotting goes!
cheers!
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