Can a non-profit organization operate under the umbrella of another non-profit business?

Can a non-profit organization operate under the umbrella of another non-profit business?
Yes. If you are an arts organization there are several non-profit organizations that act as fiscal sponsors for arts groups allowing them to apply for grants and accept donations ear marked for their purposes. They usually keep 3 - 10% of the donations.

But any non-profit organization can act as an umbrella for another non-profit group if goals are similar.