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This is represented in the game already by the Imperium government type, but you can change the title of "Imperator" to "Princeps" in localisations\vae_victis.csv if that helps (just search the file for Imperator).

If you want an entirely new government type to better represent the principate as a kind of monarchy-led republic, then that would take a lot of modifying events and laws and such. It's something I'm currently tinkering with for EITC :)
 
In a way that I'm not yet ready to reveal :) It's going to be a pretty major feature of EITC, so I won't go into details but the Principate government type would be a Monarchy type that still has republican titles (though they'd all be represented by minor titles). Some of those titles will give characters the right to propose laws and the like, and others the power to veto them...
 
May be this doesn't work or isn't what you want, but could it be a solution to make the Imperium a republic with the ruler's term set to a hundred years? This way, you basically have a ruler for life, with the consul election representing the selection of the next Princeps.
 
May be this doesn't work or isn't what you want, but could it be a solution to make the Imperium a republic with the ruler's term set to a hundred years? This way, you basically have a ruler for life, with the consul election representing the selection of the next Princeps.
Even better, you can set the ruler to have a term of -1, which the game translates to a lifetime term. The only problem is that you won't have actual dictatorial powers in that there will still be actions that the senate will block. My solution for this will be to automatically make the dictator temporary friends with all of the faction leaders, which should make the senate agree to anything.