Having indexes doesn’t affect performance, in general, they are meant to improve performance of query filtering and sorting operations. Having lot of indexes for a collection can affect write performance - this is because when a document is written (inserted, updated or deleted) the indexes are also updated. Also, indexes need to be in RAM memory for them to be effective.
That said, you can have multiple compound indexes and these can be used as needed for filtering and/or sorting operations. Make sure that an appropriate index is in use for an operation by generating and verifying a query plan on the query.
Also, see this topic on Sort and Non-prefix Subset of an Index.