Can I renew my 60-day visa exemption and extend my stay in Thailand after returning from Laos?

Note: Once you exit Thailand, that VISA stamp you entered with is no longer valid. You can get another 60-day VISA exemption when you return. Once you return with your new 60-day stamp, you can extend for an additional 30 days at the Immigration Office to total 90 days.

You can still apply for a 30 day extension on each entry.

There is no more 2x per year land border limit. That was abolished with the new 60 day visa exempt.

Each entry is at the discretion of immigration. If they feel you are abusing tourist entries then you are likely to encounter issues. You say you've already entered visa exempt 2 times. Most people begin to encounter issues around 6 months in Thailand, so if you are getting close to that you might want to start considering a visa.