Halliday & Matthiessen (2014: 665):
(i) On the one hand, there are semantic domains that range over more than a single grammatical unit. Thus the semantic domain of modality is realised in more than one place in the grammar; for example, it is realised by ‘mental’ clauses such as I suppose and by ‘relational’ clauses such as it is possible, by verbal groups with finite modal operators such as may and by adverbial groups with modal adverbs such as perhaps. These modal patterns within different grammatical units are not interchangeable synonyms; they have distinct values within the overall semantic system of modality. As we shall see below, while the forms above can all realise ‘low probability’, I think is explicitly subjective, it is possible is explicitly objective, may is implicitly subjective and perhaps is implicitly objective. This means that the semantic system of modality is more extensive than the modal features of any one given grammatical unit would suggest; it is realised not by a single grammatical unit but by a range of units: semantic unit a ↘ grammatical units m, n & o.