A key notion in understanding language is ‘possible word (lexeme)’. While there are lexemes that are internally homogeneous and externally consistent, we find others with splits in their internal structure (morphological paradigm) and inconsistencies in their external behavior (syntactic requirements). I first explore the characteristics of the most straightforward lexemes, in order to establish a point in the theoretical space from which we can calibrate the real examples we find. I then schematize the interesting phenomena that deviate from this idealization, including suppletion, syncretism, deponency, and defectiveness. Next I analyze the different ways in which lexemes are ‘split’ by such phenomena. I set out a typology of possible splits, along four dimensions: splits that are (i) based on the composition/feature signature of the paradigm versus those based solely on morphological form; (ii) motivated (following a boundary motivated from outside the paradigm) versus purely morphology-internal (‘morphomic’); (iii) regular (extending across the lexicon) versus irregular (lexically specified); (iv) externally relevant versus irrelevant: we expect splits to be internal to the lexeme, but some have external relevance (they require different syntactic behaviors).
I identify instances of these four dimensions separately: they are orthogonal, and therefore not dependent on each other. Their interaction gives a substantial typology, and it proves to be surprisingly complete: the possibilities specified are all attested. The typology also allows for the unexpected patterns of behavior to overlap in particular lexemes, producing some remarkable examples. Such examples show that the notion ‘possible word’ is more challenging than many linguists have realized.