With interleaving, the multiple boost circuits aren't completely independent. If they use current mode control, then they will have independent current control loops, but the voltage control loop will be shared between them. That ensures inherent power sharing. That's why there are specialized ICs for current control loop (they also handling the splitting of the clock for each phase). It's generally possible to make two completely independent converters with their own control ICs work in an interleaved fashion, but you have to ensure power sharing and phase shift yourself.
I wouldn't get too hung up on the whole interleaving thing, it's just an idea I tossed out there. To be frank, if you don't understand what the benefits and drawbacks are, then you can't really justify using it for yourself. Also there are very few suitable controller ICs, and most of them will be pretty sophistocated and specialized. With some quick searching the closest thing I was able to find was the UCC28220, which might work for your application. I don't have time to browse the entire datasheet myself though.