No cheap options, but here is what I would consider:

https://www.drivekyte.com/ is a newer option.

https://turo.com/ has discounts for monthly rentals, though you'll need to choose a super cheap car (think: 2015 Corolla) to get it under $900/month.

https://www.volvocars.com/us/care-by-volvo/ gets you a new Volvo on a short-term lease. One all-inclusive payment includes insurance and maintenance too. Though the minimum term is 4 months.

https://www.swapalease.com/ allows you to take over and finish out someone else's lease. A lot more legwork than the rental options, and probably not worth it for only 3 months.

Traditional rental car companies do longer-term rentals and you should call a few of them, but there is an extreme demand/supply imbalance in the car rental industry right now as people are starting to travel again and the rental car companies are thin on fleets. So expect these to be pricey but call to ask.

The cheapest, but much more complicated option, is to buy a used Corolla and sell it when you're done with it. I wouldn't do this for only 3 months, and it is best suited for the type of person who really knows the ins- and outs of buying and selling used cars.

Wondering if anybody here has experience with long term car rentals. We will need an extra car for 3 months, and are trying to explore all options.