S1613, Trastuzumab and Pertuzumab or Cetuximab and Irinotecan Hydrochloride in Treating Patients With Locally Advanced or Metastatic HER2/Neu Amplified Colorectal Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * STEP 1 INITIAL REGISTRATION: HER2 TESTING * Patients must have histologically or cytologically documented adenocarcinoma of the colon or rectum that is metastatic or locally advanced and unresectable * Mutation results: * All patients must have molecular testing performed in a Clinical Laboratory Improvement Act (CLIA) certified lab which includes which includes KRAS and NRAS gene and exon 15 of BRAF gene (BRAF V600E mutation); patients with any known activating mutation in exon 2 \[codons 12 and 13\], exon 3 \[codons 59 and 61\] and exon 4 \[codons 117 and 146\]) of KRAS/NRAS genes and in exon 15 (BRAFV600E mutation) of BRAF gene are not eligible * Patients must not have been treated with any of the following prior to step 1 initial registration: * Cetuximab, panitumumab, or any other monoclonal antibody against EGFR or inhibitor of EGFR * HER-2 targeting for treatment of colorectal cancer; patients who have received prior trastuzumab or pertuzumab for other indications such as prior history of adjuvant or neoadjuvant breast cancer treatment prior to the development of advanced colorectal cancer are eligible * Patients must not have had history of severe toxicity and intolerance to or hypersensitivity to irinotecan or any other study drug; patients must not have had a severe infusion-related reaction during any prior therapy with pertuzumab or trastuzumab * Patients must have tumor slides available for submission for HER-2 testing; HER-2 testing must be completed by the central lab prior to step 2 randomization * Patients must be informed of the investigational nature of this study and must sign and give informed consent in accordance with institutional and federal guidelines; for step 1 initial registration, the appropriate consent form is the step 1 consent form * As a part of the OPEN registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system * STEP 2 RANDOMIZATION * Patients must have HER-2 amplification as determined by central testing (3+ or 2+ by immunohistochemistry and HER-2 gene amplification by in situ hybridization with a ratio of HER-2 gene signals to centromere 17 signals \>= 2.0) * Patients must have measurable disease that is metastatic or locally advanced and unresectable; imaging used to assess all disease per RECIST 1.1 must have been completed within 28 days prior to step 2 randomization; all disease must be assessed and documented on the Baseline Tumor Assessment Form * Patients must have had at least one prior regimen of systemic chemotherapy for metastatic or locally advanced, unresectable disease; patients must have progressed following the most recent therapy; prior treatment with irinotecan is allowed; for patients that received adjuvant chemotherapy: prior treatment for metastatic disease is not required for patient who experienced disease recurrence during or within 6 months of completion of adjuvant chemotherapy; if the patient received one line of adjuvant treatment and had disease recurrence after 6 months of completing chemotherapy, patients will only be eligible after failing one additional line of chemotherapy used to treat the metastatic or locally advanced, unresectable disease; patients who have received \>= 3 lines of systemic chemotherapy for metastatic or locally advanced, unresectable disease are not eligible * Patients must have completed prior chemotherapy, immunotherapy, or radiation therapy at least 14 days prior to step 2 randomization and all toxicity must be resolved to Common Terminology Criteria for Adverse Events (CTCAE) version (v)4.0 grade 1 (with the exception of CTCAE v4.0 grade 2 neuropathy) prior to step 2 randomization * Brain metastases are allowed if they have been adequately treated with radiotherapy or surgery and stable for at least 30 days prior to step 2 randomization; eligible patients must be neurologically asymptomatic and without corticosteroid treatment for at least 7 days prior to step 2 randomization * Patients must have a Zubrod performance status of 0 or 1 * Patients must have a complete physical examination and medical history within 28 days prior to step 2 randomization * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 75,000/mcL * Hemoglobin \>= 9 g/dL * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) both =\< 5 x institutional upper limit of normal (IULN) * Bilirubin =\< 1.5 mg/dL * Calculated creatinine clearance \> 30 ml/min within 14 days prior to step 2 randomization * Patients who have had an echocardiogram performed within 6 months prior to step 2 randomization must have ventricular ejection fraction (left ventricular ejection fraction \[LVEF\]) \>= 50% or \>= within normal limits for the institution * Patients must not have an uncontrolled intercurrent illness including, but not limited to diabetes, hypertension, severe infection, severe malnutrition, unstable angina, class III-IV New York Heart Association (NYHA) congestive heart failure, ventricular arrhythmias, active ischemic heart disease, or myocardial infarction within 6 months prior to step 2 randomization * Patients must not have any known previous or concurrent condition suggesting susceptibility to hypersensitivity or allergic reactions, including, but not limited to: known hypersensitivity to any of the study treatments or to excipients of recombinant human or humanized antibodies; patients with mild or seasonal allergies may be included after discussion with the study chairs * Patients must not be planning treatment with other systemic anti-cancer agents (e.g., chemotherapy, hormonal therapy, immunotherapy) or other treatments not part of protocol-specified anti-cancer therapy including concurrent investigational agents of any type * No prior malignancy is allowed except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, ductal carcinoma in situ, other low grade lesions such as incidental appendix carcinoid, or any other cancer from which the patient has been disease and treatment free for two years; prostate cancer patients on active surveillance are eligible * Patients must not be pregnant or nursing; females of child-bearing potential must have a negative serum pregnancy test within 7 days prior to registration; women/men of reproductive potential must have agreed to use an effective contraceptive method while on study and for at least 7 months after the last dose of study treatment; a woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months; in addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation; however, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * Patients must be given the opportunity to consent to the optional submission of tissue for future research * Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines; the appropriate consent form for this registration is the step 2 consent form * STEP 2 RANDOMIZATION: As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Patients must have documented disease progression while on CETIRI (Arm 2) on this protocol; the Follow-up Tumor Assessment Form documenting disease progression must be submitted to Southwest Oncology Group (SWOG) prior to step 3 crossover registration; registration to step 3 crossover must be within 28 days of discontinuation of CETIRI protocol treatment; patients going off treatment for any other reason are not eligible * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Patients must have a Zubrod performance status of 0 or 1 * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): ANC \>= 1,500/mcL * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Platelets \>= 75,000/mcL * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Hemoglobin \>= 9 g/dL * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): AST and ALT both =\< 5 x institutional upper limit of normal (IULN) * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Bilirubin =\< 1.5 mg/dL * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Calculated creatinine clearance \> 30 ml/min within 14 days prior to step 3 crossover registration * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Patients must have left ventricular ejection fraction (LVEF) \>= 50% or \>= lower limit of normal for the institution by echocardiogram within 14 days prior to step 3 crossover registration * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Patients must have a magnesium, potassium, calcium, sodium, bicarbonate, and chloride performed within 14 days prior to step 3 crossover registration * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines; the appropriate consent form for this registration is the step 2 consent form * STEP 3 CROSSOVER REGISTRATION (OPTIONAL): As a part of the OPEN registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system