What is the best way to transport a group of 12-15 people for a weekend trip without booking multiple cars?

I saw you're asking about transport for a wedding/trip. For a group of 10+, I’d highly recommend looking for a Tempo Traveller on Rent.
In my experience, a 1x1 Maharaja seating configuration is the most 'luxury' feel for guests. Just make sure the driver is experienced with hill driving if you're headed to the mountains. I used India Tour Taxi last month for a 12-seater; their drivers were punctual and the AC was top-notch. It’s usually better than the local 'stand' drivers because you get a proper invoice and digital tracking.