Within human microbiomes, Gracilibacteria, Absconditabacteria, and Saccharibacteria, members of Candidate Phyla Radiation (CPR), are increasingly correlated with human oral health and disease. We sought phages that are capable of infecting these bacteria, as these may prove effective for phage therapies to control oral microbiome composition. To do this we analyzed spacer inventories from CRISPR-Cas systems that themselves could be used for phage editing. Absconditabacteria and Gracilibacteria recode the typical TGA stop codon to glycine and are infected by phages that share their host's alternate genetic code. Unexpectedly, however, other predicted phages of Gracilibacteria and Absconditabacteria do not use an alternative genetic code. Some of these phages are predicted to infect both alternatively coded CPR bacteria and the standard code host bacteria upon which the CPR bacteria depend. These phages rely on other stop codons, and thus should be capable of producing viable gene products in either bacterial host type. Interestingly, we predict that phages of Saccharibacteria can replicate in Actinobacteria, which are likely the Saccharibacteria hosts. Overall, this broad host range behavior may be advantageous for the production of CPR phage therapy agents, as non-CPR bacteria are easier to cultivate than CPR bacteria. Absconditabacteria and Gracilibacteria phages may have avoided acquisition of in-frame stop codons to increase the diversity of bacteria in which they can replicate.