If the War of the Roses have taught us anything, there will always be pretenders plotting when there is a not a clear and strong successor.
The Princesses Lavigny or Duval could become Empress and no need to remove the winner as a Power.
If they were then to fall into turmoil for a period or even collapse* then a perfect organic way for a war for the throne to start.
This might be beyond 1.4 though
I don't think the Emperor's Dawn will be a new power, but becomes the front for one of the losing ones in the Imperial Power Struggle, for the sole reason of "use the Ultra Nationalist/extremists to over throw my enemies" we see often in history
Though I could understand an Imperial power reshuffle, as currently the four are the possible contenders to the throne, once the succession crisis ends, they might be reorganized into the Crown Faction and a Senate Faction, vying for control, akin to the Two parties of the Federation.
The Alliance could so with an opposition party to methinks
Though how that would work in game, with a reshuffle I dont know.
If there is a new Player Power from a Minor Player faction, I'd like to see the first one be one of the Independents.