intermingle with (someone or something)
To join, mix, or blend with other people or things. A noun or pronoun can be used between "intermingle" and "with." Can you please make sure that our new student intermingles with the rest of the class at lunch? I've intermingled your suggestions with the existing curriculum. Do you think Sam will be able to intermingle with the group? He can be pretty standoffish.
intermingle something with something
to mingle or merge things with things. Don't intermingle the U.S. mail with the interoffice mail. The office mail had been intermingled with the regular mail!
intermingle with someone
to mingle or merge with people. The mugger intermingled with the people on the street and could not be recognized. Let's intermingle with the guests.