Modify an existing non clustered index or create a new index in SQL Server 2012

I have a table with 150 million records and 8 indexes. One of the indexes is on userId. A lot of the current queries I have filter on userId and therefore this index works perfectly. For one of the queries, I have to expand the where clause to include regionId and productId columns. I have two options: I can create a new index with (userId, regionId, productId) or add these new columns to the existing index. Which would be a better option? If I modify the existing index, would it affect the other queries that already use userId? **My Goal:**
I want my current query which expands the where clause to include RegionId and productId to run faster but I don't want my other queries that only have userId in the where clause to be affected. If I add a new index on (userid, regional, productid) I can accomplish that but I'm not sure if I'm duplicating the index since I already have an existing index on userId which I can expand to include regionid and productId. But I'm not sure about the consequences of modifying the existing index. Thanks for your time!