Multi-course ouds and lutes of course predate anything resembling the modern guitar by a long, long way. Do you consider those in the “guitar family”? If so, I’d refer to the group as oud or lute family. Guitar family is a recent subset of lute family, and doesn’t even contain the first multi-course instruments.

https://en.wikipedia.org/wiki/Category:Guitar_family_instrum...

https://en.wikipedia.org/wiki/History_of_lute-family_instrum...