I had over a dozen short-term stays in Brazil where I flew into GRU (on AA) and departed again the next day or sometimes even the same evening.
Never any immigration issues, just a ton of passport stamps (my passport allows visa-free travel to Brazil, though). In case of flight delays we could leave the terminal again several times and were escorted back through immigration so the dog could go outside again - no trouble at all (try that in the US...)
I always walked between T3 and T1 (traveling with a dog). The shuttle buses tend to be very full during peak hours.
Here's the relevant secion of the GRU website: https://www.gru.com.br/en/passenger/...rport/transfer