There's a couple of possible approaches I can see here. Looking at the source code, it seems the dnnModal always has an ID of #iPopUp. So, you could target it with script immediately after it's opened, e.g.
That would add class="foo" to the modal.
Another possibility would be to use a completely different modal script, instead of the built-in one. For instance I've worked on sites which have a theme based on Bootstrap. With those I've been able to use the Bootstrap modal and customise it to my heart's content.
(note the link is to the Bootstrap 4 documents - Bootstrap 3's modal works slightly differently)