How to handle "none" category?

I am trying to make my model robust against pictures that are not related to a category i’ve trained on.
For example I try to classify houses based on their architecture but an image of a dog is also seen as a particular house.
To avoid the softmax end activation, I am using a multilabel classification model (end activation is sigmoid and binary crossentropy loss fuction.) so I can already find out how much the image is related to each category.
Does anyone have experience with this?