There indeed are. The one I am most familiar with is the philosophy of Helmuth Plessner, especially in his book The Levels of the Organic and the Human [Die Stufen des Organischen und der Mensch] from 1928. The English translation by Millay Hyatt and an accompanying commentary are soon to be published.
A very (and too) short description
The following is VERY superficial. In my current work, it takes around 30 pages to explain the core concepts and ideas needed to understand how all this is supposed to work at all.
The whole book starts out with the Cartesian dualism and how it necessarily arises out of the philosophical analysation of common intuition: As we only have access to the objective world through our sensations of it, which are in turn also "only" appearances in the subjective sphere, there seems to be an insurmountable divergence of inner and outer being, of the "true being" (Kant's thing-in-itself) and the appearances of it we can get hold of. (pp. 41-50)
His criticism of empirical (natural) sciences is that they are stuck in an inner tension: Firstly, every scientific description has to start from the phenomenal reality of appearances (even if the appearances are mediated through experimental instruments etc.). Then, natural sciences go on to describe physical conditions of the possibility of occurrence, and state that this description is a description of "objective reality" of the outer world. Secondly, the very dichotomy between inner and outer world, between subject and object, relies on the Cartesian dualism and implies the impossibility of ever getting hold of objective reality.
A classic example used by Plessner is the scientific description of the qualitative sensation of a colour as merely being the neuronal signals in our brain induced by electromagnetic radiation of a certain wavelength hitting our retinal cones (29–30): the immanent reality of a quality is reduced to the “objective” physical conditions of its occurrence, while the subjective conditions that also are conditions of the occurrence of the very same phenomenon of “redness” would lead to mere illusions. Science claims to fully understand the reality of the phenomenon while at the same time never being able to really explain the qualitative nature of the phenomenon (leading to epiphenomenalism - a form of shrugging your shoulders). This “one-sidedness” (75,83,108–9,111–12,186,330) of the consideration of the conditions of the possibility of the occurrence of a phenomenon – which can also fall into the other extreme of considering only the subjective conditions (i.e. philosophically idealism and as a science many branches of psychology, sociology, etc. - cultural sciences). This kind of one-sidedness, the reduction of the phenomenon to one of its aspects, is described as constituting a "plane of experience".
And as reality is not "two-dimensional" - to follow the picture of a "plane of experience" - we have a twofold task: first, to consider both physical and subjective conditions of the possibility of phenomena, secondly, to explain how it is possible to consider these two poles/aspects/divergent spheres in a way that we can conceive them as expressions or structures of one and the same unitary reality.
He himself frames the whole philosophical problem as one of overcoming the mind-body-dualism since he phrases his philosophical questions that have to be answered as follows:
[How] to comprehend the human as he lives and understands himself, as a sensuous-ethical [sensuous = physical; ethical = cultural] being in one [unitary] experiential position, appropriate to human existence and encompassing “nature” and “spirit” [?] (p. 25)
[W]hat are the layers of existence [Dasein] with which the human shares existence because of the way his being is? How does he, as a living unit, have to experience himself and the world? (p. 37)
TL;DR
Plessner develops a philosophy that questions the dualism as being a fundamental one. Dualism is just a way to look at reality, a mutually exclusive focus. And he offers an alternative: That all that there is (for the human) is that which expresses itself to him and that to which he can stand in relation with (through structural characteristics of being). In other words: Real is that to which we can(or must) behave, the single ontological reality is the process of living as both body and mind in relation to a world itself.
Clarification: How does this answer the question?
Well, Plessner indeed describes structures of reality that allow for not only an "intersection" but for an understanding of the ontologies as one-sided aspects of reality. And as soon as we are enabled to understand reality as unitary by having unfolded the conditions of the possibility to do so, it becomes clear that there is no need to contemplate about the possibility of an intersection between aspects that are only divided in our "habitual" (p.80) way to intuit [anschauen] reality. At the same time, the unity of reality is justified by showing how both ontological spheres indeed share the very same structural characteristics, which are thus - real.
