I have never heard of Darwin's 'principle of multiple utility', but several papers refer to it. For example, from Darwin at the molecular scale: selection and variance in electron tunnelling proteins including cytochrome c oxidase
Such a high degree of conservation is probably the consequence of many parallel and concurrent aspects allied to the construction, manifold functions and demolition of cytochrome c oxidase as illustrated in the molecular scale view of Darwin's principle of multiple utility (Darwin 1872) shown in figure 7.
Also, from the pape, Engineering enzymes.
Another source of biological complexity arises from Darwin's principle of multiple utility. The principle originally applied to organisms recognizes that any one trait in an organism is subject to be selected by multiple forces.
The citation to "On the Origin of Species" in these paper provides no page numbers. Neither do any of the other papers that mention the principle. I searched the sixth edition of "On the Origin of Species" for terms such as utility, multiple, roles, etc., but found nothing that sounds like such a principle.
It seems to me that anything described as a Darwinian principle would be extensively discussed in the literature. That does not seem to be the case with this so-called 'principle of multiple utility'.