the short answer is no, having multiple labels are not available for the Neo4j indexes.

There is an exception to this which is the FULLTEXT indexes, but they are the only ones that can have multiple labels for the same index.

Here is some documentation around creating vector indexes, https://neo4j.com/docs/cypher-manual/current/indexes/semantic-indexes/vector-indexes/#create-vector-index, and for the full syntax description https://neo4j.com/docs/cypher-manual/current/indexes/syntax/#create-vector-index (and to compare the fulltext one that allows more than one label: https://neo4j.com/docs/cypher-manual/current/indexes/semantic-indexes/full-text-indexes/#create-full-text-indexes and https://neo4j.com/docs/cypher-manual/current/indexes/syntax/#create-full-text-index)

/Therese