It depends how creepy and how much money.
Does anyone remember the Emperor's Assassin guy from TIE-Fighter that used to hand out side missions and objectives? How sweet would it be if the was a bit of corporate and international back-stabbing, intrigue, subversion and power-plays going on? Every once in a while a creepy guy with a briefcase full of cash and documents could show up and ask you to do side missions (wrapped into your main mission) for cash, technology, rank bonuses or promises of more funding.
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"Let the aliens kill this particular civilian. They are an enemy of our state, wanted on warcrimes charges and has fled to your country. We'll pay you $100,000 if they are disposed of by non-human hands."
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"Please ensure that the northern office block is destroyed in this action. Our corporate opposition has it's R&D HQ located there. We will offer you our advanced technologies and lab facilities for one month if you make this so."
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"With the alien war sapping the economy so greatly, our competitors in Russia are beginning to gain ascendance over us in manufacturing. Please turn a blind eye to alien activities in their sphere-of-influence to ensure they are bought down to size. We will give your troops advanced training and promote them so that they are beyond reproach for their "negligence". "
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You wouldn't have to do the side quests, but you could get ahead at the expense of your sponsors, your nation or the world itself. There could also be long term detriments (or benefits) to being the bad-guy (or the good-guy) to balance out the quick gains (or sacrifices) made. I like the idea of there being a bit of a shadow conspiracy and a war-within-a-war going on. Again, it would just make the conflict seem so much larger than a six man team vs an alien civilisation.
It wouldn't be very hard to do. 20 different types of world-map missions (essentially just yes/no responses), 20 different types of in-game missions (yes/no response and then having to do it), research missions (yes/no, must research a certain thing by a certain timeframe for a bonus but it might throw out your own research plans) and then a bit in a blurb in the monthly funding report on different countries casaulties, successes and a little extra blurb relating to the effect of some missions (world-map ones mainly). You wouldn't have a side mission every mission, they'd be randomised on protagonists, needs, targets and rewards, and a bit of a randomised report to show you made a difference no matter what your choice was. Plus bonuses/detriments in the short/long term for Xcom.
Once again procedural generation of mission objectives could save the world from feeling too small. It would be nice for not only no play-through of Xcom to be the same, but also to have a different story each time. Like a mini-Europa-Univeralis except with lasers and aliens