Alcsentre Calanice
Gone Fishin'
To be fair, they could always come to a compromise with the army, like making the Emperor head of the army but having it be officially controlled by the Senate. And limiting the powers of the Emperor is honestly a GOOD thing, as in OTL, in the words of EU4: "the autocratic, semi-divine nature of the emperor is so powerful it encourages civil wars." So with limiting the Emperor's powers, it will make the Roman Empire more stable, and if the Emperor and the Senate find a decent compromise in authority in the Empire, then you're golden.
Emperor - head of the army. This is very dangerous. The emperor could, everytime the senate opposes him, send his soldiers to Rome to restore the old order.