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In current stellar evolutionary models, the occurrence of pair instabilitysupernovae implies the lack of stellar black holes (BHs) with masses betweenabout $[60, \, 120] \, \rm{M}_\odot$, resulting in the presence of an uppermass gap in the BH mass distribution. In this Letter, we develop a fiducialmodel describing BHs beyond the pair instability gap, by convolving the initialmass function and star formation rate with the metallicity evolution acrosscosmic time. Under the ansatz that the underlying physics of binary formationdoes not change beyond the gap, we then construct the cosmic population ofmerging BH binaries. The detection rate of BH binaries with both masscomponents above the gap, is found to range between $\simeq [0.4,\,7] \,\rm{yr}^{-1}$ for LIGO/Virgo at design sensitivity and $[10, \, 460] \,\rm{yr}^{-1}$ for third-generation ground based detectors, considering the mostpessimistic and optimistic scenarios. LISA can detect individually thesebinaries up to thousands of years from coalescence. The number of eventsmerging in less than four years, which enable multi-band observation insequence, is expected in the range $[1, \, 20]$. While ET will detect all theseevents, LIGO/Virgo is expected to detect $\lesssim 50\%$ of them. Finally, weestimate that the gravitational-wave background from unresolved sources in theLISA band may be in principle detected with a signal-to-noise ratio between $\simeq 2.5$ and $\simeq 80$.

Merger rate of stellar black hole binaries above the pair instability mass gap