Can a Toyota MR2 last until 300k miles?

Sure! Why not?

A good friend of mine still has a VW Beetle in his garage that he's owned since he was a teenager, and it has done over 400k miles, and still goes like a good 'un.

The interior smells a bit bad, though.

What are possible ways to keep the car going to so long?

using common sense maintenance techniques

don't let your kids drive it...

Don't let it run out of gas.

The first generation MR2 engine was remarkable for its time. Few last more than 150,000 miles. The second generation MR2 non turbo engine is pretty long lasting and can go over 200,000 easily if well maintained and regularly serviced, especially changing timing belt at recommended mileage/time intervals (100,000 km/63,000 miles or 5 years).

The third Generation MR2 only had a 140 h.p. non turbo Corolla engine. That engine is also pretty much bullet proof. It uses a timing chain not a belt.

Perform regular servicing to makers recommendations. Do not flog the engine. Use vehicle conservatively. If buying a used one check it has a documented service history and get an independent mechanic to check it.

Three new engines and two new chassis.