I often say to Claude "you're doing X when I want Y, how can I get you to follow the Y path without fail" and Claude will respond with "Edit my claude.md to include the following" which I then ask Claude to do.
Not sure this is a great idea. The model only internalized what it was trained on and writing prompts/context for itself isn't part of that. I try to keep my context as clean as possible, mostly today's models seem smart/aligned enough to be steered by a couple of keywords.