It's usually quite possible. Movie theaters make their money on food and drink, so arranging an extra screening for the cost of 50% of the seats in a given room is nicely profitable.
Depending on the theater's manager, they'll either want someone to guarantee a minimum or to have a single fee paid up front.
There's nothing quite like knowing that everyone in the theater is a friend.
Opening night most if not all of the ticket price goes to the studio anyway, but it's the ticket price not the per-showing price - so if they have a theater empty anyway (and I've not seen a blockbuster fill all theaters at a given multiplex for decades, and even then it was only small 4plex) they might as well make you a deal.
The split on ticket price between studio and theater operators is usually around 50% for the opening period. The window scales towards the theater's benefit over time, usually going to about 75% in favor of the operator.
That said, you're 100% right about making an offer. Most theaters have underutilized screening rooms, and managers have the ability to rent for private events. I've done this a few times. The rental rate tends to be about 10-15x the price of a single ticket (in my experience).
Depending on the theater's manager, they'll either want someone to guarantee a minimum or to have a single fee paid up front.
There's nothing quite like knowing that everyone in the theater is a friend.