Bacterial biofilms, often impenetrable to antibiotic medications, are a leading cause of poor wound healing. The prognosis is worse for wounds with biofilms of antimicrobial-resistant (AMR) bacteria, such as methicillin-resistant Staphylococcus aureus (MRSA), methicillin-resistant S. epidermidis (MRSE), and multi-drug resistant Pseudomonas aeruginosa (MDR-PA). Resistance hinders initial treatment of standard-of-care antibiotics. The persistence of MRSA, MRSE, and/or MDR-PA often allows acute infections to become chronic wound infections. The water-soluble hydrophilic properties of low-molecular-weight (600 Da) branched polyethylenimine (600 Da BPEI) enable easy drug delivery to directly attack AMR and biofilms in the wound environment as a topical agent for wound treatment. To mitigate toxicity issues, we have modified 600 Da BPEI with polyethylene glycol (PEG) in a straightforward one-step reaction. The PEG–BPEI molecules disable β-lactam resistance in MRSA, MRSE, and MDR-PA while also having the ability to dissolve established biofilms. PEG-BPEI accomplishes these tasks independently, resulting in a multifunction potentiation agent. We envision wound treatment with antibiotics given topically, orally, or intravenously in which external application of PEG–BPEIs disables biofilms and resistance mechanisms. In the absence of a robust pipeline of new drugs, existing drugs and regimens must be re-evaluated as combination(s) with potentiators. The PEGylation of 600 Da BPEI provides new opportunities to meet this goal with a single compound whose multifunction properties are retained while lowering acute toxicity.