For the most part yes.
But there are some minor incompatibility among progressive presses.
For example, the lee presses require a lee seater die if you attach the bullet feeder kit.
The hornady press with a lee factory crimp die on the last station has to be modified to not interfere with the case ejector.
Old style lee dies are a pain to work with in a dillon because they're short.
If you use other than lee dies in a classic turret and load auto advance on, you'll need a extension on the lee powder measure to clear the longer dies.
And so on.....