You can negate inside the brace tests also, so to reuse your original code:
# Using || (or)
if [[ ! -f file1 || ! -f file2 || ! -f file3 ]]]]; ;then
# Do stuff with the files
fi
# Using && (and)
if [[ ! ( -f file1 && -f file2 && -f file3 ) ]]; then
# doDo stuff with the files
fi