Is it acceptable to list both a DOI and a URL in the same works-cited-list entry if one leads to a chapter and the other to the book as a whole?
No. If you are citing a chapter of a book from a novel or monograph, create an entry for the book as a whole and list the book’s URL or DOI in the “Location” slot, since in MLA style, chapters from these types of works are not cited individually:
Gerrard, Christine. Aaron Hill: The Muses’ Projector, 1685-1750. Oxford UP, Jan. 2010, doi:10.1093/acprof:oso/9780198183884.001.0001.
If you are citing a chapter from an anthology, create an entry for the chapter and list the chapter URL or DOI:
Lewalski, Barbara K. “Paradise Lost, the Bible, and Biblical Epic.” The Oxford Handbook of the Bible in Early Modern England, c.1530-1700, edited by Kevin Killeen et al., Oxford UP, Nov. 2015, doi:10.1093/oxfordhb/9780199686971.013.34.
If you are citing the anthology, create an entry for it, and list its URL or DOI:
Killeen, Kevin, et al. The Oxford Handbook of the Bible in Early Modern England, c.1530-1700. Oxford UP, Nov. 2015, doi:10.1093/oxfordhb/9780199686971.001.0001.
A DOI is preferable, but if a URL is the only location available, provide it instead.
If you cite a chapter with a URL or DOI that leads your reader to a preview of the chapter and you wish to let your reader know that the entire text of the book can be accessed through a URL or a different DOI, provide this information in a note at the first mention of the source in your work.
Read more on including a DOI for a book chapter.