Alternatives to storing a record with exactly n multiple foreign keys from the same foreign table, where the relationships can't be repeated
Are there official terms for this type of scenario?


Yes.  This is a Symmetric Relation.  And "relation" here has the same meaning as in "Relational Database".  An RDBMS is a database management system designed around storing relations.  However RDBMSs don't have a native way to store symmetric relations.  You either have to store both tuples, eg (a,b) and (b,a) as separate rows, or you have to use some sort of convention to store only one tuple.  A common approach is to use a check constraint on the FKs.

eg 

check (singular_id_1 &lt; singular_id_2)


Assuming the relation is anti-reflexive.