You could use 1 UberXL (6 riders) + 2 UberX's (4 riders). You will need to have 3 different people download the app & sign up, as each account can request only 1 vehicle at a time.
Do a Google search for "Uber promo code", and look for the promo for new riders on the official Uber.com site; it will save you a significant amount on the first ride.
Alternately, you can have one person sign up using that promo, and then have the other 2 use the first person's referral code. The first person will then get a smaller discount on the return ride, as well.
If you prefer Lyft, 1 Lyft Plus + 2 Lyfts will be the same.