yes but THE HOUSE OF REPRESENTATIVES according to the us constitution has the power to impeach:
The House of Representatives...shall have the sole Power of Impeachment.
ARTICLE I, SECTION 2, CLAUSE 5
thus to implement an impeachment inquiry or rules of impeachment, IMO the whole house must vote on the inquiry. as you say there are no standing house rules. They at that time would authorize the inquiry and its limitations and powers such as subpoenas. We have a rogue House of Representatives acting against the Constitution. Maybe we should start impeaching them starting with Pelosi and Schiff...
That wouldn't cure the fundamental defect here. There is no reasonable basis for suspicion of an impeachable action by POTUS.
Once again we are treated to government forces topping last week's excess. The government abuses its power daily in the courts, so we are somewhat accustomed to it. The Congress also steps out of bounds on legislation, so no shocker it would "play games" with impeachment too.