In any case, there have been three legally valid constitutions since the 3rd May Constitution, none of which make provision for any sort of monarchy or aristocracy.
Four, including the current one.
1. The March Constitution (1921-1935, used also, of course, with some changes, by the communist authorities after the World War 2, which didn't acknowledge the April Constitution as a legally valid since it was a result of the Piłsudski's coup)
2. The April Constitution (1935-1939)
3. The Constitution of PRL (1952-1997, it was, of course, changed in 1989, and later in 1992 to enable the change of the political system)
4. The current constitution (from 1997)