For "thing" to be used in a maximally general way requires that "thing" have a functional meaning like "whatever is referred to by a noun, no matter if it's abstract or concrete, spatial or nonspatial, causal or noncausal, etc." Then it inherits its generality from the generality of "noun referent," and yet that phrase makes reference(!) to a more specific type of word and a more specific type of semantic operation.
Or we might try out, "Things are answers to what-questions," like, "What is the sky?" or, "What is 1 + 1?" Then "thing" is as general as "what," which is quite general, but is it more general than, "Why?" or, "Which?" or, "Whether...?" Moreover, wh-terms are like variables, so have we come to the variable/constant distinction as equally general compared to "thing," or is "thing" supposed to still be more general?
A "trick" option would be to take the phrase "that which is most generalized" as that which is most generalized. One might object, "But that phrase doesn't directly refer to anything!" But if we can work with "thing" despite its ghostly qualities, why not "that which is most generalized"? Or what if we thought up the term "pre-thing"? As if to say, "X is a pre-thing if X will become a thing at time Y," or "if X is more basic than what it will become at time Y." By contriving words like "pre-thing," "ur-thing," "quasi-thing," "meta-thing," and so on, we either undermine the generality of "thing," or we show that the question of maximal generality is itself a mirage.