The Baikal-GVD deep underwater neutrino experiment participates in the international multi-messenger program on discovering the astrophysical sources of high energy fluxes of cosmic particles, while being at the stage of deployment with a gradual increase of its effective volume to the scale of a cubic kilometer. In April 2021 the effective volume of the detector has been reached 0.4 km3 for cascade events with energy above 100 TeV generated by neutrino interactions in Lake Baikal. The alarm system in real-time monitoring of the celestial sphere was launched at the beginning of 2021, that allows to form the alerts of two ranks like muon neutrino and VHE cascade. Recent results of fast follow-up searches for coincidences of Baikal-GVD high energy cascades with ANTARES/TAToO high energy neutrino alerts and IceCube GCN messages will be presented, as well as preliminary results of searches for high energy neutrinos in coincidence with the magnetar SGR 1935+2154 activity in period of radio and gamma burst in 2020.
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