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While GRB afterglows are observed in an exceptionally broad range of photon energies an observation in the hard X-ray to soft gamma-ray range is very rarely available. Part ofthe reason for this consists in limited fields of view of the hard X-ray instruments as well asdifficulty in implementation of very rapid follow-up strategies required for detection of therapidly fading afterglow.Small number of hard X-ray afterglow detections make it difficult tomake detailedpredictions for expectations of INTEGRAL follow-up of neutrino and gravita-tional wave transients which are thought to be associated with nearby GRBs.Additionally detection of the GRB afterglow in previously poorly explored energy range would provide new important information allowing approach consistent understanding ofthe complex interaction between ultra-relativistic ejecta of the GRB and the circum-burstenvironment.Finally the target of this proposal will serve as a live and practical test for the newly understood unique capacity of INTEGRAL to perform very fast slews which has a potential to provide unique early hard X-ray observations with its large FoV as demonstrated in the case of GW170817 re-pointing.We suggest to perform INTEGRAL pointed follow-up of exceptionally bright and luminous GRBs.Taking into account difficulty of rapid follow-up we only request observation inthe most favourable conditions when it is technically feasible to to start the ToO very soon after the event. [truncated! Please see actual data for full text]