In a comment under What is the “maximal hyperreal field”? a commenter put “for any first-order theory with infinite models, one can prove the following in NBG set theory with the axiom of global choice: there is a class-sized "model" ⊨ such that every type over any set-sized ⊂ is realized in . (I say "model" in quotation marks because the usual definition of model defines them as set-sized objects.) moreover one can prove this object is unique up to "isomorphism", in the sense of class functions”
Does the same theorem hold for the conglomerates of Morse-Kelley Set Theory? If so, is there any text that mentions them and can this be used to make an ordered field larger than the surreals but with the transfer principle?