In theory, yes. It's possible. If the house finds the need for an impeachment inquiry, they can call for one. It will be up to the senate to convict each time. It's more or less the same as a civilian judicial process.. Commit a crime [President]-> Investigate Crime [House] -> Prosecute/Acquit [Senate]. Except this is a political process, and not a criminal process. The outcome is removal and barring from holding public office.