Let's take a standard diatonic harmonica in C. By blowing, 3 notes are produced. C E and G. That gives us the C chord. Drawing will produce the other notes in that key - namely D F A and B. By blocking one note,(B), a Dm chord can be produced, drawing on all will make a kind of G9, albeit with no root. That's about it for one harmonica. To a great extent why cross harpists use the harp a 4th above the key everyone else plays in.
Since the choice for playing is either blow or draw, and the notes have to be arranged to produce triads at minimum, the most chords any instrument could produce would be two, with an option of a dyad for a third. I have never seen a harmonica that was built in sections in order to blow or draw in different places producing the main diatonic chords, but have no doubt they could be produced - at a cost. Then, of course, they would have to be available, like blues harps, in several keys. Sales wouldn't be high, consequently their prices would.