An Taoiseach (Irish Prime Minister)
Legifrance - Le service public de l'accés au droit - Constitution
Art. 8. - Le Président de la République nomme le Premier Ministre. Il met fin à ses fonctions sur la présentation par celui-ci de la démission du Gouvernement.
The president can only fire the PM if the PM presents his resignation. When the PM and the president come from the same party, it is traditional that the PM signs a blank resignation letter before coming into power. Auferre, trucidare, rapere, falsis nominibus imperium; atque, ubi solitudinem faciunt, pacem appellant.
Constitutionally, the president cannot remove the prime minister, but he actually can. "The womb that spawned that thing is fertile yet"
Anyway, my understanding is that it is NOT limited to when they are from the same party. "The womb that spawned that thing is fertile yet"
(runs) WHEEEEEEEEEEEEEEEEEEEEE!