Should we "double down" on an intelligence innate in the child or try to "fan out" to develop the child where he or she is weaker at?

Personally, I would do try to do both and see which "approach" the child seemed to enjoy more of. I would guess it is easier to further "exercise" what he/she is innately inclined towards since she will enjoy those activities more. That being said, no harm in exposing her to the "weaker" ones, perhaps just one at a time, so that he/she could also develop in those areas.

Well every child is different.