Once you’ve got your Companies set up (including client affiliations with those companies), you can create Groups whose client membership is defined by company.
Just create a Group as usual, and then from the Membership area click the “Membership by Company…” button.
Setting Group membership by Company means that when you add a new client to that Company, that client is automatically added into the Group. (Likewise, removing a client’s affiliation from a Company automatically removes them from the Company Group.)
There’s still flexibility, of course: you’re still free to manually add group clients who are not from the company, and remove select company clients as desired. Controls to deactivate and reactivate individual Group memberships remain in effect as well.