Being a (hands up, guilty as charged) life-long, olympic gold winning pedant, I have a personal loathing of the generic term "people carrier", which is a clumsy tautology compared with individual model designations like "+2" and "Grand".
"Multi purpose vehicle" IMHO misses the mark, too. "Able to transport people and/or luggage": Barring two-seaters, wowee, show me a car that doesn't do that! In Spain a legal quirk provides the category "Mixto" ("combination") for large vans and some cars like the Chrysler Voyager, which can be registered for the first four years as a "trade" vehicle (lower VAT and lower top speed, but six monthly MoT tests), regardless of numbers of seats or actual usage, and then re-classified. But I digress...
If it were possible to wind the clock back to the day before the first of these daringly different designs was actually launched before a gobsmacked motoring public, I'd humbly offer the alternative of "seven-seater" as a generic term. Maybe "three-row" in second place.
Any other suggestions out there?