The deteriorating effectiveness of antibiotics is propelling researchers worldwide towards alternative techniques such as phage therapy: curing infectious diseases using viruses of bacteria called bacteriophages. In a previous paper, we isolated phage EFDG1, highly effective against both planktonic and biofilm cultures of one of the most challenging pathogenic species, the vancomycin-resistant Enterococcus (VRE). Thus, it is a promising phage to be used in phage therapy. Further experimentation revealed the emergence of a mutant resistant to EFDG1 phage: EFDG1r. This kind of spontaneous resistance to antibiotics would be disastrous occurrence, however for phage-therapy it is only a minor hindrance. We quickly and successfully isolated a new phage, EFLK1, which proved effective against both the resistant mutant EFDG1r and its parental VRE, Enterococcus faecalis V583. Furthermore, combining both phages in a cocktail produced an additive effect against E. faecalis V583 strains regardless of their antibiotic or phage-resistance profile. An analysis of the differences in genome sequence, genes, mutations, and tRNA content of both phages is presented. This work is a proof-of-concept of one of the most significant advantages of phage therapy, namely the ability to easily overcome emerging resistant bacteria.