Can Quantum Field Theories Exhibit S-Dualities with Distinct Lagrangians?

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Hi folks: I have a question on dualities. Does anyone know of a QFT with a (conjectured) S-duality, such that the two classical theories corresponding to that QFT have very different Lagrangians? That is, such that the two classical theories that define the QFT cannot be expressed as essentially same Lagrangian but with the elementary and composite fields interchanged in each case?

I'd really appreciate an example -- or also to know if it isn't possible. Thanks!
 
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