The phrase "several invitations" means receiving a number of requests or offers to attend or participate in different events or activities. Full definition
He also stands accused for refusing to appear before the committee after several invitations. (citifmonline.com)
I received several invitations to give lectures on how to use the Internet for forensic science in those days. (sciencemag.org)
However, I had to decline on several invitations to join people for trips, tours, lunch and coffee because I made plans already. (probearoundtheglobe.com)