How can I extend a 90-day volunteer visa in Chiang Mai for an additional 35 days?

You can't just extend non immigrant categories for 30 days with no documentation like a tourist entry. You'd have to be still volunteering, and the extension would typically be longer, and the documentation and process are a lot longer, and would need to be supported by your volunteer organization as Robert says. I believe with volunteer visa extensions they go "under consideration" for a period while they think about it. I am guessing from your post that the volunteering is probably finished and you probably won't be going through a full volunteer extension, which is an involved process.

If they only need 35 days your best bet is probably to do a border run to Mae Sai at the end of the current 90 days. You can then extend that normally for 30 days without documentation as a tourist entry. That will get you 60 days which is >35.

If the volunteer organisation can support the application with all the correct paperwork it should be no problem.