Modify tag query to also includes results from a category

I would like to modify the results of the tag query e.g.:

/tag/dog

so that it also included posts that are in the category “dog”

If I try to add the category into the pre_get_posts filter when a tag query is being made it produces a query that requires both the tag and category to be matched whereas I want either the category or tag.

Any ideas?

Thanks for any help.

Julian