Working with large groups …
Discussion market, open space, world café, … you name it. Invent your own terms for working in interactive ways with large groups!
We have decades of experience with working with large groups. The largest group I aver had was a group of 800 managers in the Meistersinger Halle in Nürnberg. We had 20 facilitators to make participants work in a very interactive way during 2 days.
Working with large groups is specifically important when you want to start a change-project, when you want to make sure that all people get informed/involved within a short time frame. The idea is to involve people already in early stages, not just to inform them but to catch their ideas. It is by far more efficient and effective to run a few workshops with large groups than just sending announcements or giving a speech in front of 1.000 people with several thousand others in further locations video-watching the managers presenting charts.
Of course, to be able to run large events you need facilitators. You may engage external facilitators/trainers. But you may also train some of your managers/professionals to be facilitators. Build a pool of facilitators!
Working with small groups …
We also work quite often with very small groups. E.g. 4 managers with 1 trainer in a 3-days-workshop. Or even: 9 participants with 3 trainers in a 3-days-seminar. Of course this is quite expensive for you. But if you think in terms of training and in terms of transfer, you will see that it pays off.

Think in terms of Return-on-Training and Transfer, not budgets!