Is it possible to have a global prettify-symbols-alist that other modes add to? A lot of major modes override prettify-symbols-alist instead of pushing into it. One solution I thought of is to push the global entries in a hook that runs after the buffer and its mode have initialized. I don't know of such a hook, unfortunately.
Modes usually inherit from each other. For example,
java-mode inherits from
prog-mode which inherits from
fundamental-mode. Similarly, many modes inherit from
special-mode. If you add a function to both
special-mode-hook, you should already cover many major modes.