Is it okay to enter Thailand multiple times on a visa exempt basis for short stays?

Get a tourist visa for the middle one just to be safe and avoid any potential questions. You’ll be fine though

If you get the 60 day visa exempt stamp and extend by a further 30 days at the Immigration office, Immigration class you as a tourist. If you then attempt to enter again on a visa exempt stamp, Immigration rightly consider that after on 90 day stay in the country that you are no longer a tourist but that you are attempting to live long term in the country. While there is no legal limit to the number of Visa exempt entries, once the Immigration officer believes that you are no longer visiting the country as a tourist he will deny you entry. If you have already stayed for 90 days on a visa exempt entry, then in future to guarantee entry into Thailand, you need to obtain a long term visa suitable to the reason for your stay.

Out of interest: Thailand has recently cracked down on foreign nationals abusing visa-free entry. Between January and May 2025, immigration officers denied entry to approximately 8,193 foreigners, many suspected of entering under the guise of tourism to work illegally.