There is a built-in assumption in this question that needs immediate clarification. To assign a social motive to the sonnets (i.e. love statements) is to diminish their function as poems. That is, we are confusing modern-day love poems (think greeting cards), whose purpose is to declare or otherwise articulate emotions to someone (“Shall I compare thee to a summer’s day?”), a direct utterance sent to a recipient. While scholars can build arguments for a “dark lady” or even a male lover, the sonnet’s actual raison d’etre is probably independent of an actual” love interest” on Shakespeare’s part. First, they were written over a long period of time, and only gathered in 1609, well past both Shakespeare’s London career and the vogue of sonnet-writing.
Most telling is that subsequent editions all arrange the sonnets in different orders, so that what appears as an emotional clustering of the poems is nothing more than a publisher’s attempt to make order out of arbitrariness. And it is this arbitrariness that guarantees contradictions in the sonnets. They are, in fact, all the many facets of the subject of human emotions, written over a lifetime, not a single statement from one point of view. They are in fact poems, concentrated word magic, using all the elements of language available to the poet – rhyme, meter, figurative language, metaphor, etc. – to ring the changes on the subject. The word “contradict” is entirely too reductive. Not sure what you mean by “3 main characters,” but assuming you are referring to the division by some editors into “poems to a young man” (the first 126 in the Thorpe edition,) “poems to a mysterious Dark Lady (127-152), and “a friend, possibly a colleague,” the division is quite arbitrary and definitely post-facto. Consider "Two loves have I of comfort and despair." A better area of inquiry is the echoings in the dramas of motifs in the sonnets.