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You can make grep -v work with multiple strings. For example:
$ cat patterns.txt
xxx
yyy

$ cat input.txt
jjj
ggg
xxx
yyy

$ grep -v -f patterns.txt input.txt
jjj
ggg
Make your pattern...

Great. Yes, the -f option is pretty basic, so I'm glad you found a grep that supports it.

in that case egrep should help.

egrep -v "sent to primary BE|CC-Request-Type 3 received in state Idle|Unknown session-id. Origin-Host" /var/adm/messages* | wc -l