This. I have a particular fondness for the unfortunate Alexander Severus. Perhaps it was the sad way in which his death was described in Edward Gibbon's 'Decline and Fall'.
I agree that Septimius would need to leave the throne to one of his children, not both. The other would be shortly killed after this no doubt. Geta was popular with the soldiers, but Caracalla more devious (?) Actually if Septimius lives a little longer the natural death of one of his sons in battle might occur if Scotland is fully pacified and conquered. The conquer of Scotland alone would have interesting long term butterflies by itself, even if the succession goes much as it did in OTL.