Do you change the participants? Does the methodology change when you have a constraint like a participant time crunch? Is the methodology always applied the same way for all types of problems?
As a facilitator, you take what you are given but often if you’ve got a chance to bulk up the team at the beginning, you might try to get a mix of styles. However, don’t forget, these styles are preferences not skills and a very good facilitator is someone who will take what’s there and move the group through the process. By involving people early in doing the profile to build their understanding, they get the idea that we’re supposed to be moving around the wheel, no matter whether we’re this or we’re that. Furthermore, we are going to work together to make it work knowing these are “states” not “traits” and you make it happen. If you only have a small amount of time you might find out that your team is heavy in one style versus another so you might, if you only have four hours, spend an hour on the part they they prefer to do like implementation and spend three hours on part they least prefer so you can you can make things happen your own way. By engaging the team, they will help you make it work because they understand the process.
The method does not change regardless of the problem. But you might have to “flex” the process depending on the particulars of a problem. The process remains absolutely the same, but how you make it work, how you flex it depends on the situation you’re in. You invent new tools if you have to but the process itself and all the phases remain the same. Always trust the process so the process is going to work for you. This is exactly what we teach and focus on in our Professional Innovation Advisor (PIA) program.