Let R be an integral domain, and let A,A1,A2,…,As be overrings of R, where A is of the form S−1R, where S=R∖𝖕1∪⋯∪𝖕n for some prime ideals 𝖕i, and where each Ai, i≥2, is of the form for some multiplicatively closed subset Si of R. It is shown that if A⊆A1∪⋯∪As, then A⊆Ai for some i.