While the interaction problem now is taken as a soul-body problem, in the rationalist authors it’s clear that it is a part of a much larger question about the whether extension is substantial, and if it is, in what way it is.
Descartes: The substance of things in the physical world is their extension. There are many substances and so many extensions. Minds are non-extended, but the relationship between mind and extension is undefined and problematic. The interaction problem is arises here.
Malebranche: There are not many, but only one substance of the physical world: extension. Thus, the lines dividing the finite extended things Descartes’s world disappear and we get one substance: infinite, uniform, mathematical. Mind is ontologically prior to extension, to the extent of being able to preserve its properties even if God annihilated the physical world. The substance of the physical world is seen in God, though M. takes great pains to articulate the causal relation from God to this extended substance that is seen in him. All minds are prior to extension, and the divine mind is that in virtue of which the extended both is and is known by finite minds.
Leibniz: The extended cannot be substance but can only proceed from some unextended substance – the monad. As in Descartes world, we have many substances again, but extension is not their substance. As in Malebranche’s world, extension is projected into the world from non-extended realities, but it loses its substantial character.
D: Many extended substances, many unextended substances; M: One physical substance, extension, which is seen in the unextended; L: there is no extended substance, only a projection from many unextended substances.