You can probably use EXISTS filters to get at a lot of this. However, it would depend on how you identify these requests, which isn't clear in your original post.
For example, if each of your requests uses a unique custom form, you can filter on projects which do not have a request that has custom form A or custom form B (or both).
If the requests use a standard and consistent title, same: projects that do not have a request with title ABC or XYZ.
Or if the requests utilize unique queue topic names.
It's difficult to give you a more specific answer without some more information though -- as you can see, I've listed three different ways to submit these kinds of requests and each would be a different type of filter.