My own opinion about Pushkin, but others can chime in. I think that Dallinger is really optimized for these iterated experiments, and Empirica is really optimized for group interactions. I don't know whether we are going to support either, simply because I think Dallinger and Empirica do those things well, and they require very different tech from the more "viral quiz" method that gameswithwords and testmybrain specialize in. Zooniverse, too, does annotations very well, so I don't see a reason to reinvent that wheel.
Of course, this may change. I know that the devs behind Empirica, Dallinger, and Pushkin have been talking off-and-on about doing more code-sharing and making the projects work together better.