If your version of grep accepts the -P option, you can use grep -a -P to search for an arbitrary binary string inside the binary. This is close to what you want:
grep -a -c -P '\xFF\x84\x03\x07' myfile.bin
Unfortunately, grep -c will only count the number of "lines" the pattern appears on, even if it appears several times in a line. (I'm not sure why this would be a desirable feature).
To get the exact number of occurrences using grep , you need to do:
grep -a -o -P '\xFF\x84\x03\x07' myfile.bin | wc -l
grep -o splits each match into its own line, and wc -l counts the lines. Note that this depends on the fact that your binary string does not contain strings.
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