Inclusion Criteria: -PRE-REGISTRATION: Age >= 18 years. -PRE-REGISTRATION: Clinically or histologically confirmed diagnosis of second-generation antiandrogen-refractory metastatic castration-resistant prostate cancer. -PRE-REGISTRATION: Measurable disease as defined by the Prostate Cancer Working Group (PCWG3) criteria. -PRE-REGISTRATION: Prior treatment required: -Second generation anti-androgen (2GAA) therapy (e.g., enzalutamide, abiraterone) at any time prior registration. -PRE-REGISTRATION: Provide written informed consent. -PRE-REGISTRATION: Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study). -PRE-REGISTRATION: Ability to complete questionnaire(s) by themselves or with assistance. -PRE-REGISTRATION: Willingness to provide mandatory blood specimens for correlative research. -PRE-REGISTRATION: Willingness to provide mandatory tissue specimens for correlative research. -REGISTRATION: Plasma NRG-1 level >= 4 ng/ml -REGISTRATION: Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2. -REGISTRATION: Hemoglobin >= 9.0 g/dL -REGISTRATION: Absolute neutrophil count (ANC) >= 1500/mm^3 -REGISTRATION: Platelet count >= 100,000/mm^3 -REGISTRATION: Total bilirubin =< 1.5 x upper limit of normal (ULN) -REGISTRATION: Alanine aminotransferase (ALT) and aspartate transaminase (AST) =< 3 x ULN (=< 5 x ULN for patients with liver involvement). -REGISTRATION: PT/INR/aPTT =<1.5 x ULN OR if patient is receiving anticoagulant therapy and INR or aPTT is within target range of therapy. -REGISTRATION: Calculated creatinine clearance >= 45 ml/min using the Cockcroft-Gault formula. -REGISTRATION: Left ventricular ejection fraction (LVEF) >= 50% =< 15 days prior to registration. -REGISTRATION: Provide written informed consent. -REGISTRATION: Ability to complete questionnaire(s) by themselves or with assistance. -REGISTRATION: Willingness to provide mandatory blood specimens for correlative research. -REGISTRATION: Willingness to provide mandatory tissue specimens for correlative research. -REGISTRATION: Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study). Exclusion Criteria: -PRE-REGISTRATION: History of myocardial infarction =< 6 months prior to pre-registration, or congestive heart failure requiring use of ongoing maintenance therapy for life threatening ventricular arrhythmias. -PRE-REGISTRATION: Failure to recover from acute, reversible effects of prior therapy regardless of interval since last treatment. -EXCEPTION: Grade 1 peripheral (sensory) neuropathy that has been stable for at least 3 months since completion of prior treatment. -PRE-REGISTRATION: Uncontrolled intercurrent non-cardiac illness including, but not limited to: -Ongoing or active infection -Psychiatric illness/social situations -Dyspnea at rest due to complications of advanced malignancy or other disease that requires continuous oxygen therapy -Any other conditions that would limit compliance with study requirements -PRE-REGISTRATION: Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy. -NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial. -PRE-REGISTRATION: Receiving any other investigational agent which would be considered as a treatment for the prostate cancer. -PRE-REGISTRATION: Thromboembolic event =< 60 days prior to pre-registration. -PRE-REGISTRATION: Serious cardiac illness or medical conditions including, but not confined to, the following: -History of NCI CTCAE v5.0 Grade >= 3 symptomatic congestive heart failure (CHF) or New York Heart Association (NYHA) Class >= II -High-risk uncontrolled arrhythmias (i.e., atrial tachycardia with a heart rate >= 100/min at rest, significant ventricular arrhythmia [ventricular tachycardia], or higher-grade atrioventricular [AV]-block, such as second-degree AVblock Type 2 [Mobitz II] or third-degree AV-block) -Serious cardiac arrhythmia or severe conduction abnormality not controlled by adequate medication -Angina pectoris requiring anti-angina medication -Clinically significant valvular heart disease -Evidence of transmural infarction on electrocardiogram (ECG) -Poorly controlled hypertension (e.g., systolic > 180 mm Hg or diastolic > 100mmHg) -PRE-REGISTRATION: Serious cardiac arrhythmia or severe conduction abnormality not controlled by adequate medication. -PRE-REGISTRATION: Angina pectoris requiring anti-angina medication. -PRE-REGISTRATION: Clinically significant valvular heart disease. -PRE-REGISTRATION: Evidence of transmural infarction on electrocardiogram (ECG). -PRE-REGISTRATION: Poorly controlled hypertension (e.g., systolic > 180 mm Hg or diastolic > 100mmHg). -PRE-REGISTRATION: History of ventricular dysrhythmias or risk factors for ventricular dysrhythmias, such as structural heart disease (e.g., severe left ventricular systolic dysfunction [LVSD], left ventricular hypertrophy), coronary heart disease (symptomatic or with ischemia demonstrated by diagnostic testing), clinically significant electrolyte abnormalities (e.g., hypokalemia, hypomagnesemia, hypocalcemia), or family history of sudden unexplained death or long QT syndrome. -REGISTRATION: Any of the following because this study involves an agent that has known genotoxic, mutagenic, and teratogenic effects: -Pregnant persons -Nursing persons -Persons of childbearing potential or able to father a child who are unwilling to employ adequate contraception -REGISTRATION: Failure to recover from any of the following therapies prior to registration: -Major surgery -Chemotherapy -Infection requiring systemic treatment -REGISTRATION: Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. -REGISTRATION: Immunocompromised patients and patients known to be HIV positive and currently receiving antiretroviral therapy. NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial. -REGISTRATION: Uncontrolled intercurrent illness including, but not limited to: -Ongoing or active infection -Symptomatic congestive heart failure -Unstable angina pectoris -Cardiac arrhythmia -Or psychiatric illness/social situations that would limit compliance with study requirements. -REGISTRATION: Currently receiving any other investigational agent which would be considered as a treatment for the primary neoplasm. -REGISTRATION: Other active malignancy =< 3 years prior to registration. EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix. NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment (e.g., other hormonal therapy, chemotherapy) for their cancer. -REGISTRATION: History of myocardial infarction =< 6 months, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias. -REGISTRATION: Known hypersensitivity to pertuzumab, or trastuzumab, or hyaluronidase, or to any of its excipients. -REGISTRATION: Requirement for drugs or substances which can interfere with the actions of the study drugs (enzalutamide or pertuzumab/trastuzumab/hyaluronidase-zzxf). Consult pharmacist for review.