No - you can only get one offer. You will fill in a form that lists your choices and send it to the borough you live in (even if some of the schools listed on it are in other boroughs or other counties). On offers day, you will be offered the highest ranked school that your DD qualifies for. If she qualifies for all the grammar schools she sits for, she will be offered a place at the one highest up on the list you filled out. None of the others will offer her a place.
I am thinking of entering my dd for the 11+ exam next year. She will probably be taking exams in two different boroughs. I just wanted to know whether it is possible to receive an offer from different schools in different boroughs?