You do what they do in TV shows. Make part of the show as cheaply as possible - a bottle show or near to it - and save the budget for later when you need it.
Start on the ship set with only the regular cast. Have them go somewhere, beam some down to an Earth like planet. Have them get in trouble. Have them deal with it while something happens on the ship.
So far, you've saved on expensive guest stars, used existing ship sets and natural environments. You haven't hired Idris Elba, spent a fortune on the Yorktown design and effects, the swarm, destroying the Enterprise and a huge planetary set, and you're still at about the same point of the film. Use plot and acting to get you there, then use the savings to pay for a more spectacular final act. It still doesn't need to be quite as over the top as Beyond.
Save even more by seeing which cast members would accept reduced salaries in exchange for % points...
I'm sorry ?
Beyond was (surprisingly, given that Pegg wrote it) stylistically identical to the previous two. No improvement whatsoever...
Nailed it. They could easily do a tense 'balance of terror' type movie that would be like, say 'crimson tide' that would absolutely rock for 100 million.