I'm looking for an adjective, and thesauri have failed me. I'm trying to create the sense of "nothing can be added to this thing", which the words "complete" and "incorrigible" don't capture. Like if I was talking about two people who were in a "happy, complete and __ relationship", if I wanted to describe the relationship as so perfect that it needed no improvement. I thought I was onto something with "unameliorable", but I haven't been able to find any dictionary entries for it, nor on wiktionary.
In questions like these, it takes some work to find a correct word. First, I'm going to check the dictionary, then find some synonyms and finally study their semantic connotations.
From Dictionary, the first meaning of complete is: - having all parts or elements; lacking nothing; whole; entire; full.
In other words, if something is complete, nothing can be added to it, because it has all parts and lacks nothing. This matches exactly your description.
As for the meaning of perfect, I think we are more looking at meaning 4.: - entirely without flaws, defect or shortcomings.
Therefore, I believe you are asking for synonyms in the region between complete and perfect, which may imbue more of the emotional values that you are looking for. You can find Synonyms and Hypernyms from Synonym Finder.
One word that kept appearing was "consummate" (adj.) with first meaning as adjective: complete or perfect, superb; in the second: being of the highest or most extreme degree.
An expression like "a consummate relationship" would then entail one that contains all necessities to make it perfect, and nothing can be added.
Another synonym I like was "pure" meaning that nothing can be added, lest it become impure. So, this word implies a measure of "maximal simplicity", of having everything necessary, but not more. This is often said of "a pure love".
The next step would be to find semantically related words (not necessarily synonyms), to get a feel of the word you are looking for. Here follow the lists from English Synonym Finder for the words in question. You can do your own additional research.
Semantic representation of "perfect" includes the following words: absolute, accomplish, accomplished, accurate, achieve, adept, ameliorate, arrant, better, boost, bring to perfection, clean, complete, completed, consummate, correct, crown, elevate, enhance, ennoble, entire, exact, excellent, exemplary, expert, faultless, finish, finished, flawless, fulfil, full, ideal, immaculate, impeccable, improve, infallible, intact, irreproachable, make perfect, matchless, mature, mellow, model, perfect, polish, precise, pure, refine, ripe, skilled, superlative, total, unblemished, unerring, unmitigated, untarnished, upgrade, uplift, whole
Semantic representation of "complete" includes the following words: absolute, accomplish, accomplished, achieve, aggregate, all, all over, all-out, arrant, clean, clinch, close, complete, comprehensive, conclude, concluded, consummate, dead, discharge, dispatch, do, downright, effect, end, ended, entire, execute, exhaustive, fill in, fill out, finalise, finalize, finish, finish off, finished, fulfil, full, get done, get finished, give the final touch to, give the finishing touch to, ideal, implement, intact, integral, mature, out-and-out, outright, over, perfect, perform, plenary, put the final touch to, put the finishing touch to, rank, realise, ripe, round, round off, settle, sheer, solid, sound, terminate, terminated, thorough, thoroughgoing, total, unabbreviated, unabridged, unbroken, unconditional, uncut, undivided, unlimited, unmitigated, unqualified, unreserved, utter, whole, wind up, wrap up
Here is a summary of common words in both semantic representations above: absolute, clean, complete, consummate, entire, fulfil(led), full, ideal, intact, mature, perfect, ripe, total, unmitigated, whole
Words I like: elevated beyond improvement, noble, ideal, total, whole (and the earlier pure and consummate)
Words I do not like: with -less, im-, un- ; in spite of their meaning, they point to the opposite you want to express, but this need not be a "polar" opposite and therefore is too vague.
Now we can look at the semantic representations for these and I find some more words that could be used to describe such a relationship:
pure -> honest, wholesome, angelic elevated -> majestic, noble, sublime ideal -> paragon (paragonal is not a word, but you may get away with it). total -> absolute
As an example of what this can be used for, consider:
Their relationship was an absolute paragon of pure, total and fulfilling love: consummate, wholesome, majestic, angelic. :-)
I'm sure you can come up with more suitable descriptions for the relationship in question.
"fulfilled" might fit the bill. Or to be completely unambiguous and straight about it, just say "perfect".
If those do not suit then perhaps these slightly more adventurous attempts will:
"heavenly", "sublime", "beatific", "idyllic"
The adjective consummate is not all that common, amd probably sounds a little unnatural outside its collocations (consummate ease, professional, liar ...).
Copacetic: in excellent order or completely satisfactory.
very good; excellent; completely satisfactory