The Republic of Ireland has
Uachtarán na hÉireann (president of Ireland),
an Taoiseach ("Chief", "Chieftain", prime minister) and
an Tánaiste ("heir to the chief", vice-prime minister).
The First Minister of Wales is known as
Prif Weinidog Cymru in Welsh.
The Kingdom of Hungary's royal steward was known as the palatine (
palatín,
palatin) and as the centuries went on, they were not only the right-hand men of the monarch and had plenty of power of their own (and powerplays), but increasingly shifted into being a prime minister equivalent. I have a nod at this in my Carpaverse stories, where the Carpanonian head of state is the palatine (they're essentially a noble's republic, or a monarchy without a royal family - central European in tone, but with a Golden Age Dutch style setup to their politics).
In our old, award-winning
Countries of an Alternate World 2* map game from 2012-2013, I created several countries. One small central European monarchy had a palatine as its prime minister, the ruler was a king or queen. An African confederative republic I made up had "presiding chairmen" as the presidents of the two countries/entities in the confederation, in addition to a first minister and a confederal main president. Another federal southern African country had the Federal President, Constituent Presidents (also known as
mmusi, i.e. "governors" in SeTswana) and a Federal Chairman. The president of another of my African countries, a Berber-Tuareg federation, was the "Steward of the Tamazgha Tawshete". An alternate Bhutanese monarchy I included in the setting had a "Head Advisor to the King" in the prime minister role. My native-majority Taymyr politia (i.e. republic) in north Siberia had fairly inventive titles, such as "Highest Chieftain of the Politia" (president) and "Guide of the Council of Tribes" (prime minister). Other people also made up various neat political titles for that AH setting.