No. The map sources are a curated list, not something you can extend yourself. The older desktop TrailRunner let you hand-edit a configuration file inside the application. TrailRunner Mini has no equivalent.
More sources are available than you may have seen. Show More in the base-map picker reveals additional sources beyond the default set. Several strong regional ones are among them. See which maps you can use.
Tip: check there before concluding your area is not covered.
Please tell me. Good regional map sources are hard to find from the outside. A source that is excellent in your mountains is likely excellent for everyone else who goes there.
Send a link via the contact form. It can then be considered for a future version, properly cached and attributed, for everyone.