We present a theory of an interference process that starts with N coherently pumped two-mode parametric down-conversion (PDC) sources, whose output modes are directed to N observers such that each observer receives modes from two different source crystals. Each observation station is equipped with a locally controlled PDC crystal, coherently pumped with the source crystals, whose output modes are perfectly aligned with the input modes from the source PDCs. By varying the local phases of the input modes, perfect 2N -photon interference can be observed in 2N single-photon registrations, one in each output mode of these N local PDCs. The interference results from the indistinguishability of the origins of the detected 2N photons: either they all originate from the source PDCs or from the local PDCs. Bell–GHZ nonclassicality of the process emerges when one also considers situations in which at least one of the local PDC processes is blocked. In such cases, the 2N -photon interference disappears. A “lifted” Clauser–Horne inequality is violated when its sole negative term, involving all observers with all local pumps active, is tuned to maximal destructive interference, while all other terms involve settings in which one of the local pumps is off.