Outside of Toki Pona, there haven't been any "majorly" successful attempts at making an oligomorphemic language — as far as I know. While derivational and inflectional morphology could be done away with (and its information load transferred to syntax I guess), the question is how many semantic morphemes is too few before a language becomes incomprehensibly vague.
I'm guessing the theoretical lowest lower limit is the set of 63 semantic primes of the Natural Semantic Metalanguage (see also Goddard's Oxford Handbook of Linguistic Analysis, 2010). Wierzbicka and Goddard propose that you could theoretically explain almost all necessary concepts by building up from this set of primes, and lacking ways to express some of them will leave you incapable of expressing at least a subset of all possible topics.