The final distinction we will need, or more accurately, family of distinctions, is between internal and external relations. What makes them members of a single family is that a relation is internal if its holding between things is somehow fixed by the things themselves or how those things are; external relations are relations whose holding between things isn’t fixed this way.
SEP (emphasis mine)
The traditional external relations correspond to relations that are intrinsic to their pairs, but not intrinsic to their relata.
Menzies, on singularist theories. Non-singulairst theories which say that the relation between causal pairs is extrinsic, and set by the rest of the world:
Suppose I drop a piece of sodium into a beaker of acid, which event causes an ex- plosion to take place. The intuition emphasised by singularists is that the causal rela- tion holding between these events depends entirely on the local character of the events and the process which links them; and does not depend on anything else happening in the world. For example, suppose that another person is waiting in the wings, ready to drop a piece of sodium into the beaker of acid if I do not. Does the presence of this alternative cause, which would come into play if I do not drop the sodium, make any difference to whether the causal relation exists between my dropping the sodium and the explosion? The singularists argue that it does not: the presence of an alternative cause is neither here nor there to the causal relation that exists between the actual cause and effect. The causal relation does not depend on any other events occurring in the neighbourhood: the causal relation is intrinsic, in some sense, to the relata and the process connecting them.
Is it possible to conceive of a non-singularist analysis of causation that is internal? That the actual cause and effect are not all there is to the causal relation, and this involves the regularity as it appears elsewhere, so that the relation of causation is extrinsic; but still the cause and effect are intrinsically related.
Relations intrinsic to their relata correspond to the traditional internal relations. For example, the internal relation of congruence of shape is intrinsic to its relata in this way
It would have drawbacks, but does anyone talk about it ever at all? I think the advantage would be that then causal powers "do not have their origins in any kind of sensory impression" (Menzies on Hume) but nevertheless do intrinsically bring about their effect with no further explanation needed.