What’s the opposite of “singleton”?

Simply compound non- (negation) and singleton to get non-singleton, which will be readily comprehended by anyone who knows singleton. For example, in a hand of cards, you can refer to a non-singleton king and it will be understood that there is at least one other card of that suit in the hand.

In English, it is common to express meaning using compounds. In particular, there are many productive prefixes and suffixes which can be meaningfully compounded with a root word.

The term commodity can mean

a mass-produced unspecialized product: commodity chemicals

It is used to distinguish a thing that is available in multiple quantities and whose units are intercangheable as opposed to something that is unique.

Adjective fungible means “Able to be substituted for something of equal value or utility; interchangeable, exchangeable, replaceable”. For example, dollars in a bank account are fungible. For that matter, dollar bills themselves typically can be exchanged with others without making any difference, and may be thought of as fungible.

(This answer addresses the “group member that is not distinct from the other group members” portion of your question. For the “opposite of singleton” part, consider non-singleton or perhaps replicate or replicated.)