Tam Lin by Pamela Dean! There are romances and shifting alliances in this book, but the trio of roommates -- Janet, Molly, and Tina -- are brought together at the beginning and, despite their ups and downs, remain the core of the story.

Also the Newford series by Charles de Lint; it has a very large cast of characters, but he keeps returning to three friends who have been through a lot together: Jilly, Wendy, and Sophie. Probably the best book about their relationship is "The Onion Girl", but it is a theme that winds through many of the books and short stories set in this universe.

I'm sure I could think of others, but these are the ones that immediately come to mind. Also, I am wholly on board with you repurposing the word 'triumvirate' to refer to your crew. Or maybe you could play with it to make it refer to three women? I'm afraid I don't know enough about Latin roots to make a specific suggestion, though.