In my view, at the moment, this is partially possible.
Dynamic meshes (I assume you will need adaptive mesh refinement) are under development, potentially coming in preCICE v3 later this year: Dynamic Meshes · GitHub (cc @fsimonis)
Multiphase FSI with interFoam and CalculiX and static meshes is already possible. A tutorial for that is under review (on my list at the moment): https://github.com/precice/tutorials/pull/279
If this is a project without time pressure (e.g., you are now starting your PhD), you could already start by setting up a static mesh and gradually add features later.
If you want a simple and documented solution right now, this is not available.
Note that both FSI and multiphase are challenging problems by themselves, so coupling them could have unexpected challenges as well.