Here are what I consider the Big 6 vocal harmony groups. I’ve included a recommended album to kickstart your listening.
In chronological order:
The Hi-Lo’s (1953-1981) – Listen to Suddenly It’s The Hi-Lo’s
The Singers Unlimited (1971-1983) – Listen to A Cappella I
The Manhattan Transfer (1975-2023) – Listen to The Manhattan Transfer Live
The Real Group (1984-present) – Listen to Live in Stockholm
New York Voices (1987-present) – Listen to Sing! Sing! Sing!
Take 6 (1987-present) – Listen to Take 6
Dates are tricky, but these are roughly correct, based on historical founding date and/or earliest recordings.
Each has a distinct sound and approach to writing, recording, and performing. There are many other important vocal groups, but if you can recognize and speak to the characteristic sound and musical approach of these six, you should be able to effectively sing most vocal jazz/close harmony.