I don't care for the Obligation mechanic. I don't like having a mechanism that's built around reducing a score to avoid penalties (especially as group Obligation goes >100). Instead, I'm looking at reworking Duty (found in the Age of Rebellion Beta) for use in Edge since it's a system that builds upward towards rewards.
However, for this to work, it would require that the PCs have ties to a larger organization similar to Obligations like Dutybound and Sponsorship (found in Enter the Unknown). This doesn't seem too unusual, since any of the following should be appropriate:
Black Sun
Bounty Hunters' Guild
Hutt Clan (various)
Local/System/Sector Criminal Syndicate (various)
ISB
Rebel Alliance
CSA
Local/System/Sector Government (various)
Corporation (various)
University (various)
This would mean that complications that are normally associated with Obligation are now handled more freely by the GM and players as they arise. It should be possible to have Duty scores to one or more organizations, but there is always a risk that you'll be pulled in cross directions. It's also possible to stay totally independent, but this also means that there is no mechanical reward available as there is to those that fulfill their Duty.
I'm also considering tracking each character's Duty score individually, with that individual gaining a personal reward from the organization each the score reaches 100 and is 'cashed in' rather than a group reward. This would show the competitive nature of these organizations, and it's quite possible that some group members will pull more than their share and should be rewarded appropriately. Of course, clever characters might be able to steal the credit for some of their companions' contributions, but such is the politics of working in the shadows.