The theory of two-nucleon transfer reactions is extended to include higher-order transitions going through intermediate nuclear states produced by inelastic scattering of the ingoing or outgoing particle. The reaction, as is usual, is treated to first order, but the inelastic processes are treated to all orders among the retained channels. The theory is formulated so that it is very easily applied to any microscopic structure calculation, since the relevant content of such calculations appear in the theory only through the values of the matrix elements of the pair-creation ${\left[d^{†}{d}^{†}\right]}_J$ and scattering ${\left[d^{†}\tilde{d}\right]}_J$ operators.

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