You inquire of someone.
"Where do you live?", he inquired of Mike.
You inquire about something.
He inquired about items for sale.
You use inquire after to ask about the health of (someone).
He inquired after his parents.
You use inquire for to ask to see or speak to (someone).
Mike was here inquiring for you.
You use inquire into to investigate or look into something.
The police are inquiring into the causes of recent political events.
And, you could inquire with people, freedom, power, respect, eagerness, etc.
"He will inquire with more earnestness, and decide with more impartiality."
"We inquire about, and we inquire with; we inquire about various objects of inquiry, and we inquire with fellow inquirers"
"And first we must inquire with respect to the moon, in what manner that motion blends relations or natures with the moon. But this we do not see prevail except in the monthly repairing of the moon, for the periodical course of six hours"
Ref. some definitions come from Oxford dictionary.
