Position or goal grabs typically are a form of uprising (usurpal from the rightful owner) if you can say that with villian goals, if its a singular artifact they want to steal, you can just deny it and pick it up/plot against the villian at a later date.
If its against your companions interests, when they find out they might try to attack you based on any number of variables, meaning you might want to pick up some more morally ambigious characters to take with you beforehand.
That is not an uprising, more like what we call a coup; that is a small number of already powerful people plotting to seize the ultimate power above them. This is different from a mass uprising where the aim is to get as many people as possible to simultaneously seize the objective in opposition to the people in charge. They are not however an absolute difference, there is considerable overlap between the two concepts in practice. If you break down an uprising it is really reducible to a lot of separate conspiracies (in DF terms) that have joined together since they have the same general objective and the uprising then frequently breaks down into infighting as the different conspiracies find they don't really share any goal anymore.
For instance some evil vampire wants to get rid of some tyrannical king because he wants to be king instead. The plot fails causing the vampire and his plotters to be tracked down and imprisoned. However as they are being transferred to the jail, other rebellious elements mover to rescue the vampire and the original plotters release the vampire with his first group of plotters in order to thwart the king. Once the people see that the king has been successfully defied, all sorts of other groups jump on the bandwagon and the tyrannical king is overthrown.
At this point the vampire makes himself king supported by his followers, but the others were only supporting the vampire to get at their king. They don't want a vampire to be king and so the uprising breaks apart. There is also the element of the supporters of the deposed tyrant, they don't want to be punished for their crimes/keep their power and wealth and if the conflict is set to result in a deadlock they make sign up with one faction or the other. In effect they are a conspiracy with conservative aims, they aim to keep what they already have and by banding together they can lever influence by better exploiting divisions among what are actually their enemies to prevent their enemies from actually harming them.
I imagine your companions will be as morally ambiguous as you are considering you'll be able to freely swap between them.
People you pick up later might react differently though.
The people we pick up later is what I was referring to. If you sign up to certain goals, your NPC companions ought to launch conspiracies against you and potentially depose you, taking over your group with not only it's property but it's reputation. But if there are only a few NPC companions they should instead leave since they have no chance of winning an prospective uprising.