As the body wood is a fabricated wood and the stripes are a result of dyeing/staining in the manufacturing process, I have my doubts as to how well it will take more staining. All the builds I’ve seen so far have just put clear over the body.
I’m wondering if the body wood is very composite-like with a lot of glue or resin holding wood fibres together, much like an engineered fretboard. In which case staining may not work well or look very patchy. You only really have the control cavity to do any test staining on, which isn’t easy, but I’d certainly give it a go.
I’d be tempted to use a coloured lacquer rather than a stain, as that will happily sit over the top of the wood.