I recently watched a few lectures about these things.  There is disagreement over whether they actually flooded the Colosseum.  Some Roman source (I believe it was Martial) says that they did, but modern scholarship has argued that this was simply impossible to have done.  However, there is evidence in at least one other amphitheaters within the Roman Empire that shows the structure was set up to allow for flooding.In Rome, there was a gigantic area for naumachia (mock naval battle) built by Augustus (I think the same one you refer to as being by the Tiber).  I mean so large that the naumachia would consist of something like 60,000 persons in ships for the recreation.  In the lecture I watched, the professor said that there's a hardware store in Rome where you can go downstairs and see part of the remaining wall of this particular stadium. Romans also imported large quantities of exotic animals to use as part of their entertainments.  One of the events in their amphitheaters was for animal hunting and they would slaughter large quantities of birds, big game cats, elephants, or other creatures.  A system of capturing, transportation, and storage was developed over time.  I imagine that many ocean creatures died in the process.

Here is a direct quote from the lecture outline that was provided:"The substructures of the Colosseum that were integral to its functioning would have made submersion unlikely."  ..."The only amphitheater in the vicinity of Rome that was plumbed for water in the arena seems to be that at Capua."In the lecture, I think he spoke specifically about means of getting water into the theater, and also a drainage system to remove it.  Without either, flooding would be rather unlikely.  I don't recall anything about a new level being added to the Colosseum.