What if Mark Antony won the War of the Second Triumvirate and took over Rome, with Cleopatra as virtual empress?
At a great stretch, he might make Cleopatra a Roman citizen (Herod was, for example) and marry her legally, but she would never rule or exercise power as an Empress. Emperor, or rather, Imperator, was a military commander. Octavian was originally referred to as Dux but preferred the less aggressive Princeps as his casual title, holding onto the Imperator as his prename highlighting his unique position as supreme commander of the Roman military.
Say Mark Antony wins at Actium. He'll need to return to Italy, provide for his veterans, reward his allies and recruit new troops for endeavours elsewhere. Most of the old nobility was on his side, the remnants of the Liberatores, Pompeians and some of the Caesarians. He'd be able to get rid of Octavian's municipal creatures quite easily and reconcile the more useful Caesarians with ease also (ie, Asinius Pollio). Similar to Octavian his first recourse would probably be to hold the consulate fairly often and distribute provinces among loyal trustworthy men.
Lepidus, Ahenobarbus, Crassus and Pollio would be strongmen of the new regime perhaps.
Agrippa and Maecenas would most likely be ruined - proscriptions perhaps?
Antony himself had abolished the office of Dictator but he'd have need of some kind of general custody of the commonwealth (cura rei publicae) - Cassius had been made proconsul over all the East before Antony was triumvir, so it's possible he'd receive some extensive grant of imperium over a vast provincia similar to Octavian OTL. OTL Octavian blocked publication of Antony's conquest of Armenia - here he would be able to publicize his victories and nab a triumph, a nice re-entry into the Roman conscious.
Ultimately he'd need to defeat Parthia - a ridiculously draining undertaking he seemingly was unable to execute but most likely unable to let go as casually as Octavian did OTL.
Marriage to Cleopatra would be a problem - rejection of Cleopatra would be a problem. He needs to stay for an extended period of time in the West to fix all that went wrong during Octavian's last few years (in terms of his own public image) and he'd also need to go East to fight Parthia and pacify Cleopatra (not sure the capitol would be ready for her just yet). It's messy and probably wouldn't end well one way or another.