I would like you to do a class project. I expect them to be done individually, but if you would like to do a larger project that requires more than one person, I'm happy to discuss the idea with you.
One thing you could do is write a survey paper on a topic that is related to this class, but that we have not covered. Some possible topics are:
If you intend to do a survey, then please collect a set of papers and come see me. We will work out an appropriate depth for your survey.
You can instead try to answer some question. Here are some big fuzzy questions that might suggest to you a more narrow and doable question. Again, once you have some ideas, let's talk.
Paxos has steered clear of group membership as an abstraction. Is there some kind of small step one can take to bring some of the power of the group membership abstraction without reinventing group based programming?