Just wondering if there is an accepted opposite of this term, maybe something like 'generalis generis'?
Unus multorum means "one of many".
I gather that the phrase is comparable to "average Joe" in English, or "just one of the crowd"—the opposite of the uniqueness conveyed by sui generis. My Latin is not that solid; hopefully someone more knowledgeable will correct or confirm this. This 1814 dictionary reports:
unus multorum et de multis, is said of one, who is not distinguished for any thing, one of the vulgar.
People have occasionally used Unus multorum as a pseudonym when they wanted to publish something anonymously.
Its most famous ancient use is probably in Horace's 9th Satire. Horace has encountered a bore while walking, and he can't get rid of him. They bump into Aristius Fuscus, a friend of Horace's. Horace tries to hint that Fuscus could save him from the bore. Fuscus, somewhat laughingly, isn't going along with it:
"Certe, nescio quid, secreto velle loqui te
aiebas mecum." "Memini bene, sed meliori
tempore dicam: hodie tricesima sabbata, vin tu
curtis Iudaeis oppedere?" "Nulla mihi," inquam,
"religio est." "At mi, sum paulo infirmior, unus
multorum. Ignosces, alias loquar."
Horace: "I can't remember what it was, but I'm sure you were saying you wanted to talk about something with me in private."
Fuscus: "I remember it well, but I'll tell you at a better time: today is Passover [more precisely, a day when Jewish tradition forbids discussing business]. You wouldn't want to blow a fart at the circumcised Jews, would you?"
Horace: "I've got no worries about that."
Fuscus: "Well, I do. I'm not so strong-minded as you, I'm like most people. You'll forgive me, I'll talk some other time."
Note that unus is masculine. The feminine and neuter are una multorum and unum multorum respectively.
Since there has been no other answer, let me expand my comment into an answer.
I am not familiar with any technical term with a meaning opposite to sui generis. If you want an adjective of similar origin, there is generalis. But the best Latin word I know for this is solitus (a form of solere, see part II of the entry).
Notice that unlike sui generis, both generalis and solitus are adjectives and should be declined appropriately in use.