First thing you need to define is what makes ME compelling in the first place. I thought it (and Dragon Age) were compelling in it forced you build relationships between characters and to make hard decisions. Everything else, from the combat to aesthetics, could be interchangeable with something else. But the relationships and difficult decisions really are what I would seek to emulate more than anything else.
What followed was a fairly traditional implementation of social mechanics in modern RPGs. What I'd like to do is take a look at how a neoclassical game might handle similar challenges. (Do keep in mind I have never played Mass Effect. So the ideas I'm proposing here might not work for a game that is modeled on it.)
First, the neoclassical mantra: the rules reinforce the theme obliquely. That is, a game about exploration (like D&D) has rules that reward exploration, but not directly. So in our science-fiction game based on relationships of hard decisions, are rules are going to play off these themes without touching on them directly. We're not going to have mechanics that quantify relationships or play off those numbers.
Instead, what we'll craft is a series of mechanics that promote the building and maintenance of relationships. So our combat rules are going to give bonuses for having a lots of people helping out. Things like cover fire rules, overwatch mechanics, or air support and orbital bombardment which encourage players to build the sorts of relationships that allow them to call in all sorts of resources. Our more generic resource rules, things like gold pieces in D&D, are going to be based on your ability to call in help from various organizations. Your relationship with other law enforcement agencies, or even underworld types, give you access to people, information, and equipment you might not get otherwise. Finally, our basic mechanics for adjudicating uncertainty will give lots of really big bonuses for cooperation. Expert advice, hands-on assistance, and maybe even inexpert aid or even just the well wishes of others will give large bonuses to success.
But we won’t have any hard numbers to measure your relationship with others. That is up to you and the GM. It will probably be fairly binary; if you have a good relationship with these folks then they will help you. If not, you're out of luck. Of course, this leaves a lot to the discretion of the GM, but that's a fairly standard hallmark of the neoclassical style. It also gives players and GMs a lot of leeway in defining how relationships work, who you can have a relationship with, and how strong those relationships are. What we're interested in as crafters of the system is the utility of these relationships, not so much the relationships themselves. Some things are fun just as they are and don't need the extra help.
Hard decisions are like that. Again, we’ll leave a lot in the hands of the GM. The hard decisions come from the adventures and the situations that the PCs find themselves in. In a well-networked social space, these will invariably lead the PCs to choose sides. In making these choices they will almost certainly annoy some of the factions from whom they could get resources. Hopefully, the same choice will reinforce the relationship with another group. But that's not necessarily the case. Sometimes, doing the right thing angers everybody. Whether or not some recognize the virtue of these sorts of difficult choices is entirely up to the GM. But if you're simply moving back and forth on a sliding scale of being liked by group A or being liked by group B, that's not really a hard choice. Eventually, the players will decide that one side or the other can serve him better, and just max out their "faction" with that particular side. Really tough choices involved sacrificing something in return for doing the right thing, even when the right thing is not likely to win you points with anybody.
And our neoclassical sci-fi cop game handles this very well. Burning bridges means fewer resources. Fewer resources raise the difficulty of achieving your ends. We don't need to add anything in the mechanics to make certain choices difficult. We may offer some guidelines for the GM on how to handle such situations, but the mechanics handle their end of things pretty well all by themselves. This is the beauty of neoclassical game design. We don't have a whole lot of rules to memorize or look up in the middle of the game, but the ones that we do have reinforce our themes.