Wiktionary has a page for "double contractions" (contracting twice) https://en.wiktionary.org/wiki/Category:English_double_contractions so obviously, it is considered normal (or at least common). It's even more informal than single contractions though, which makes them quite rare outside of speech.

@Moshi thanks; I had not heard of "double contractions" and that didn't come up in my search.

I'd've thought it does :) I find myself using them every now and then - "I'd've", "shouldn't've" come to mind.

I suspect that the answer to this question will change within a generation. I use double contractions in informal writing, too, from time to time. Character-limited and time-sensitive (or perceived time-sensitive) e-messaging will likely make these an increasingly attractive option.

Similar, though not identical, are acronyms used as part of conversation - like: "IANAL, but...." Typically only in written text, but more and more turned into speech too.

I wouldn’t’ve thought there’d be a problem. ‘Twasn’t right?

@DonielF I write like this casually, but sometimes comment on it being quirky and I don't know that I've seen it outside of casual writing (like chat and email), and that got me wondering if it's a niche quirk or more widespread/accepted.

@Monica Saw this pop up to the top again. What do you consider "formally recognizing" as normative? For example, "I'd've" is actually an entry in the Collins Dictionary: https://www.collinsdictionary.com/dictionary/english/idve

@Moshi thanks; a dictionary entry is helpful. I see that says it's British informal English. Are there others too or just "I'd've"? I'm curious about the pattern (if there is one).

@Monica Cambridge Dictionary lists the 'd've contraction as it's own entry: https://dictionary.cambridge.org/dictionary/english/d-ve?q=%27d%27ve As far as I can tell, those are the only double contraction entries in those respective online dictionaries (at least, I'm not going through the entire wikipedia list to find out lol).

It is also interesting to note that Cambridge Dictionary contradicts itself: from here: https://dictionary.cambridge.org/grammar/british-grammar/contractions "We don’t use more than one contraction"

Whether it is meant to imply "in formal English", "in standard English", or "at all" is a bit ambiguous though.