I think there will be a side mission for temples where you have to go into the ruins of an old civilization to capture an old treasure to earn a reward. Or maybe a race mission where you have to catch the Fallen on Pikes while riding your Shrike and when you capture them you somehow get them to communicate to you to tell you of a big mission they were planning, so you can exterminate their plan.
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I think there will be random, minor objectives [such as hardpoint, evac, or domination] as you explore the world, based on what I've read.