Yes and no. There’s polyfidelity which means:

“Polyfidelity is a type of non-monogamous relationship in which all members are recognized as equivalent to the other partners and comply to restrict sexual and romantic relationship activities to exclusively only other members within the group.”

We’re not into that type of relationship personally and prefer it unrestricted/non-exclusive. That is where we were drawing our definition of fidelity from in this case. Apologies for the confusion.