We investigate N-th order (N > 2) photon-photon correlations for the light emitted from two strongly interacting nonidentical emitters. Collective dressed states, where non-identical emitters contain the component of anti-symmetric atomic state coupled with a light mode, can describe various photon correlations containing various N-photon real and virtual joint emissions. We show that the correlations for two non-identical interacting atoms have the advantage of being strong and long-lived due to the participation of the anti-symmetric atomic state in the dressed levels. This is an advantage over single or two identical interacting atoms. Our study shows this property in the case of real processes, where the photons are associated with specific resonances, and virtual processes, where pairs of photons are emitted jointly.
