Dog Adoption Database Design
You can have organisation, user, and location all have a reference to a common table representing something that can be an owner to a dog. Then dog can have a single reference to this table. Here is a diagram explaining.



dog.owner_id references can_own_dog.can_own_dog_id, in case that isn't clear. Each of the can_own_dog foreign keys is unique in their table, ideally  unique across all three tables.

I'm not sure if you're familiar with object-oriented programming, but the idea is similar to multiple classes implementing a single interface.

On another note, your diagram says "Users can have multiple locations", and "Dogs can have multiple locations". I think these mean to say "Locations can have many users" and "Locations can have many dogs"?