They’re fairly common but are typically only swaps with small names.When was the last time there was a 3 team trade in MLB? It happens all the time in the NBA due to the salary cap and need for a team with cap room to absorb a contract but that's not a factor in the MLB
Last big one I remember was just last offseason.
Braves got Sean Murphy from the A’s
Brewers got William Contreras from the Braves
A’s got a bunch of prospects from both teams