You may be thinking of Modified Newtonian Dynamics also known as MOND, rather than "modified theory of gravity". I think the term MOND or modified Newtonian dynamics, is higher regarded than modified theory of gravity. I do not know any textbooks on MOND off-hand, but there may be a few
I, too, am unsure as to what binbags wants, but I don't think that it is MOND. A possibility is "Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics" by Capozziello and Faraoni, which emphasizes f(R) theories of gravity, https://www.amazon.com/dp/9400701640/?tag=pfamazon01-20
This book has a brief survey of various theories of gravity in the last few sections of chapter 7, and then devotes a number of chapters to approaches to quantum gravity and quantum cosmology.
Use Amazon's Look Inside feature to look at the Tables of Contents of these books.