Currently, there are no effective drugs for the treatment of amyotrophic lateral sclerosis (ALS). Only two drugs—edaravone and riluzole—have been approved, but they have very limited efficacy. The aim of this work was to modify the structural core of the Edaravone—phenylpyrazolone moiety and combine it with aminoadamantane pharmacophore in order to expand the spectrum of its action to a number of processes involved in the pathogenesis of ALS. New conjugates of edaravone derivatives with 1-aminoadamantanes combined with alkylene or hydroxypropylene spacers were synthesized, and their biological activity was investigated. Compounds were found that could inhibit lipid peroxidation and calcium-related mitochondrial permeability, block fast sodium currents of CNS neurons, and reduce aggregation of the mutated form of the FUS-protein typical to ALS. So, the proposed modification of the edaravone molecule has allowed the obtaining of new original structures that combine some prospective therapeutic mechanisms against key chains of the pathogenesis of ALS. The identified lead compounds can be used for further optimization and development of new promising drugs on this basis for the treatment of ALS.