Can there be more types of self harm?

More than what: Some forms of self harm include cutting, burning, punching, pulling out hair, salt ; ice challenge etc.

Too many: To me, there are far too many ways in which we humans can harm ourselves. Certainly there are the physical ways dr. Fowler has shared, but the ways we think of and speak to/about ourselves can be devastating also. Plus we can stay in unsafe or harmful situations far longer than is healthy -- allowing others to mistreat us because we don't know that we deserve better. Get help if any apply to you.

There are: There are a number of types, but it's really about the purpose of the behaviors. If the intent is to harm one's self then pretty much anything can be considered.