I think there is some scope for shared powers or shared benefits. Turn undead, for example, could be a shared Divine power, and extra hit points could be a benefit that Primal characters could select.
Right now, this could be done by making a theme for each power source, but I suspect it will be difficult to come up with unique new powers. We might have to end up errata'ing some existing powers to be shared ones.
Another thought I had, after reading one too many posts about why some people don't like healing surges, is to tie the hit point recovery mechanic to the power source. Instead of having a common "second wind", the hit point recovery action is different for each power source, and "healing surges" would be the number of times per day that action can be used.
For example, the Divine Power source could have cure personal wounds, and the effect of using that power would be actual hit point recovery. The Martial power source could have adrenaline surge, and instead of recovering hit points, a martial character spends one Adrenaline Reserve (a healing surge) and gains Adrenaline Points (AP). AP fuction as HP, and any time you lose HP, you lose AP first. The total number of HP + AP is capped at a PC's full normal HP because the more wounded he is, the more adrenaline is generated to compensate. Narratively, a Martial character with 2 HP and 46 AP is badly wounded, covered in nicks, scratches and bruises and running on almost pure adrenaline.