If you clear someone to use the full length of a cross runway you automatically allow them the intersection too, thus you have given away the other runway. As such, you can only allow 1 movement at a time if you allow either runway full length, the only exception being if you give away either runway short of the intersection.
You can have an aircraft on approach to both runways at the same time, however they would be sequenced in such a way that the preceding aircraft would be clear of the intersection before you clear the subsequent aircraft to land.
In the event of a missed approach, the standard missed approaches would be designed so as not to conflict with each other, but if that was not the case essential traffic info and reduced separation in the vicinity of the aerodrome would be the fallback.