I don't much like that dictionary—its layout makes it too hard to extract particular meanings. Probably this one: 22. to invite or cause to be present as a companion or guest: We had Evelyn and Everett over for dinner.
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Hans51What do you think?To me, it sounds most like this: I do not mind Tom (Tom's) studying English.
Hans51We had Tom and Jessica helping us out.The following link may interest you. There is more than one interpretation of "have (someone) ---ing".
CalifJimThe following link may interest you. There is more than one interpretation of "have (someone) ---ing".-ingI can't believe I ever wrote such long posts!