So far with my regular grunts and my Heavy using the baton melee weapon, the game will not permit me to take any further actions with them for the rest of that turn, even if it is their first action and they have lots of AP remaining. I cannot even use Exertion to generate more AP despite them having enough Will.
The Technician is able to take further action after going all Doctor Octopus on enemies.
In order to allow the aliens to use their melee attack effectively with the current AI, their melee attack has a 0 action point cost. To stop them being able to use this multiple times, melee attacks end the turn - this has spilled over to effect the player controlled units.