`chmod` can do this by itself:
chmod -R g+o dir
> A combination of the letters `ugoa` controls which users' access to the file will be changed: [...] other users in the file's group (g), [...]
>
> The operator + causes the selected file mode bits to be added to the existing file mode bits of each file [...]
>
> The letters `rwxXst` select file mode bits for the affected users [...] Instead of one or more of these letters, you can specify exactly one of the letters `ugo`: [...] and the permissions granted to users that are in neither of the two preceding categories (o).