And then what?
There is actually a mod which will add another Septim heir, a brother to martin.
I cant seem to find it though :/
The Story however, is quite unrealistic. Even if you had another heir to rescue, he would be of no use, since the Dragonfires are gone, the Amulet is shattered so a new heir coulndt light the Fires, even if they werent trampled upon by Akatosh and Dagon.
Any septim heir would have "only" his Birthright to the Throne. There is no Requirement by the Divines to have someone with Septim Blood on the Throne.
With this Requirement ceased to exist, the Elder Council may want to give Throneright to another noble Family.
A Mod for a new Emperor would have to have some Story about how the Elder Council, i.e. Ocato figured a Method how to choose an Emperor. With both the Method of choosing beeing appreciated by at least most of the people of every Province as well as the new Emperor.
A Method which is sound and being appreciatet by everyone is one thing, but if it leads to a candidate from a Family which is known to hate Dunmers, the Province of Morrorwind would most likely declare its Independency, leading to a Independence War which could tear the entire Empire apart, as other Provinces may use the War in itself to declare Independence, for they will not want to help the Empire in a War to crush an Independance Movement.
The People of most Provinces do not like the Empire very much, so their Leaders risk being overthrown by an Revolution, if they the Peoples Sons and Daughters away to their possible death, just to help the Empire crush an Uprising far away.
This Leaders may want to split from the Empire for the own Reasons, like wanting to be the Ruler of their own Kingdom without the Empire being your Ruler.
But they will use the "I will not send the Sons and Daughters of my People to a Land far away to spill Blood in the Name of an Empire, which will have no Qualms to spill the Blood of my People in any similar Case."
Any "New Emperor" Story could have the Player in a Situation where he must proove, that being under the Rule of the Empire is well worth the Trouble.
Most Province People dislike the Empire for being "Not there when you need 'em".
"Nels the Naughty" hates the Redguard former Imperial Soldier in the same Quest, because some Years ago, Imperial Soldiers did nothing while Nels Village was being raided and his Daughter killed.
In an Event like this, Province People being attacked by EE's (Evil Enemies

) the Player could be in the Service as Imperial Agent, to be send in whenever the Need arises. To help fight of Enemies of any Kind, to assasinate enemy Leaders, to do Quests of any Kind which would fit in a "The Empire is there for you" Plot.
Possibilities for side Quests are there, too: Help a young Bosmer, who has dreamed to be in the Imperial Legion for almost his entire Life, to join the Legion. For that, you would have to disperse the preconceptions of the local Garnisons Leader. Take on a mission in which you protect the young Bosmer from beeing killed. Like in the Fighters Guild Quest where you and Maglir get to kill some thieves.
Protect the Bosmer, so he can come back alive and show the Garnison Leader he
can take care of himself and isnt your Garden variety sneaky Bosmer thief who would run away at the first sign of trouble.
Or, heres a whole new Idea: If you have done some dangerous errants for the Legion and earned the Respect of your Comrades, they may want to see how this Bosmer who wants to be a soldier fights.
So you find yourself in an Arena Kind of thing. The Soldiers already know you can fight, but they want to see you pummel the Bosmer, which would have to be essential, so you can knock him out without killing him.
The Bosmer is probably told that he can join the Legion if he puts you down.
Of course that wont happen. The Bosmer is knocked out, but the Soldiers would have a new Kind of Respect for him.
He lost the Fight, But a Bosmer without Legion Training who has the Guts to stand against the Playerchar, who could mob the Floor with every single last Legion Soldier and wont even Flinch...
Well he would deserve at least some Respect.
Would be a nice Side Quest. Not your usual "I lost my precious Heirloom thingy in the dark, monster overrun cave, please bring it back!

" And it would be easier to make, as youll just have to make some place to fight on, instead of designing an entire cave.