Inclusion Criteria:  Participant must provide written informed consent before any study-specific procedures or interventions are performed Participants are >= 18 years old at the time of informed consent. Both men and women of all races and ethnic groups will be included Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 Histologically or cytologically-proven adenocarcinoma of the exocrine pancreas with locally advanced or metastatic disease Must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 Must have at least one disease lesion that is amenable to biopsy procedures performed per institutional standards Must have progressed on, been intolerant to, or refused systemic therapy that is consistent with institutional standards (e.g., Gemcitabine-based, or fluorouracil, irinotecan, leucovorin and oxaliplatin [FOLFORINOX]) Must not have received any systemic therapy or other investigational agents within 30 days or 5 half-lives (whichever is longer) from first dose of study therapy Hemoglobin: >= 10.0 g/dL with no blood transfusion within 28 days of starting treatment White blood cells (WBC): > 3 x 10^9/L Absolute neutrophil count (ANC): >= 1.5 x 10^9/L (> 1500 per mm^3) Platelet count: >= 100 x 10^9/L (> 100,000 per mm^3) Creatinine =< 1.5 x upper limit of normal (ULN), or measured or calculated creatinine clearance >= 60 mL/min/1.73 m^2 for participants with creatinine levels > 1 x institutional (ULN) Serum bilirubin: =< 1.5 x institutional ULN Aspartate aminotransferase (AST)/alanine aminotransferase (ALT): =< 2.5 x ULN Participants of childbearing potential (POCBP) must agree to abstain from sexual intercourse or use effective non-hormonal methods of contraception starting with the first dose of study therapy through 90 days after the last dose of study therapy (because calaspargase pegol can render hormonal contraceptives ineffective) POCBP may participate provided they have a negative serum pregnancy test at screening and a negative serum OR urine pregnancy test within 7 days of starting treatment  Exclusion Criteria:  Concomitant use of other anti-cancer therapy (chemotherapy, immunotherapy, hormonal therapy (hormone replacement therapy is acceptable), radiotherapy (except for palliative), biological therapy or other novel agent) or live virus and live bacterial vaccines while receiving study medication Prior treatment with an L-asparaginase therapy Known severe hypersensitivity to calaspargase pegol-mknl (or equivalent) or to cobimetinib (or equivalent), or to any excipient of these medicinal products, or history of allergic reactions attributed to compounds of similar chemical or biologic composition to calaspargase pego-mknl or cobimetinib Use of known strong CYP3A inhibitors (e.g., itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir), known strong CYP3A inducers (e.g., phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate CYP3A inducers (e.g., bosentan, efavirenz, modafinil) within 7 days of prior to initiating study treatment or on going requirement for these medications Uncontrolled serious thrombosis  Uncontrolled severe or symptomatic coagulopathy; exclude if:  Prothrombin time (PT) >= 1.5 x ULN, or International normalized ratio (INR) >= 1.5 ULN, or Fibrinogen =< 0.75 ULN  Known history of chronic pancreatitis or recurrent acute pancreatitis, or at time of screening evidence of acute pancreatitis, defined by at least two of the following:  Clinical symptoms of upper abdominal pain Serum amylase or lipase that is >= 3 x ULN Imaging evidence (computed tomography [CT], magnetic resonance imaging [MRI], ultrasonography)  Significant cardiac disease within 6 months prior to start of study treatment, including any of the following:  New York Heart Association class III or IV, Congestive heart failure, acute coronary syndrome, and/or stroke, or Left ventricular ejection fraction (LVEF) < 40% by echocardiogram (ECHO) or multigated acquisition (MUGA) scan obtained within 28 days prior to start of study treatment  Known risk factors for ocular toxicity, consisting of any of the following:  History of serous retinopathy History of retinal vein occlusion (RVO) Evidence of ongoing serous retinopathy or RVO at screening Uncontrolled hypertension, or hypertension that cannot otherwise be clinically managed before initiating study therapy Participant is known to have dysphagia, short-gut syndrome, gastroparesis, or other conditions that limit the ingestion or gastrointestinal absorption of drugs administered orally Participant has active uncontrolled systemic fungal, bacterial, or viral infection (defined as ongoing signs/symptoms related to the infection without improvement despite appropriate antibiotics, antiviral therapy, and/or other treatment) Participant has corrected QT (QTc) interval (i.e., Fridericia's correction [QTcF]) >= 450 ms or other factors that increase the risk of QT prolongation or arrhythmic events (e.g., heart failure, hypokalemia, family history of long QT interval syndrome) at screening Psychiatric illness/social situations that would limit compliance with study requirements Any concurrent severe and/or uncontrolled medical condition (e.g. uncontrolled diabetes, infection, hypertension, etc.) Participant is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 90 days after the last dose of trial treatment Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirements