I currently work in a small development team that works for multiple clients simultaneously. Some of the work is developing new software for these clients and some of the work is supporting the clients with any problems they have with our software.
Does anyone have any suggestions of a lean/agile process that could be used to manage this workload for a team of 6?
If not lean, is there any other project management method that would help manage this work?
I would recommend a mixed practice called scrumban.
As you need to manage small group of people who are doing project and support work at once, you would not want sprint based approach like in scrum because your support will ruin them. Or you cannot split those two because you do not have clear team boundaries between support and development. Scrumban offers nice techniques like planning on demand and is a little bit loose compared to scrum, but that is what you would want. I have tried many practices and this one is the best for highly dynamic environment. Still it will maintain team workload and transparency in your projects.
