When a noun is modified by a verb + {-meH], the verb can act like an infinitive, as in {pe'meH taj}. But why would this always have to be the case? If the speaker wants to be more specific, as in {qaSuchmeH 'eb} "the opportunity for me to visit you," why not? Why would it always have to be {SuchmeH 'eb} "the opportunity to visit"? (And with null prefixes, this phrase can also have the more specific meaning "the opportunity for him/her to visit him/her/them" or "the opportunity for them to visit them.")

Also, in some cases the verb + {-meH} may also need the  {-lu'} suffix. This seems to me like it's necessary if the noun modified by the verb + {-meH} is the thing acted upon, as in, for instance, {qIplu'meH DoS}.

~mIp'av