Page 20 in the corebook states
Once you’ve selected a focus for a particular recursion, it doesn’t change
Contrariwise, as Caleb points out, a sidebar in page 55 offers
Each time you return to a recursion, your GM might offer you the choice of picking a focus that’s different from one you had last time you visited.
As for draggable foci, page 52 states
Some foci are draggable. This means that if you start with a focus in its proper context, you can keep it when you translate to another world. You’re “dragging” your focus with you. If you have a draggable focus but decide to change your focus when you translate, you cannot regain the draggable focus again unless you return to the original world to which it is tied. From there, you can drag it again if you wish.
Which is not for or against reassigning a focus.
So that's, those are the RAW, and the suggestion for houseruling. Apart from bookkeeping, I don't see a problem with doing it.