Inclusion Criteria:

          -  Age >= 18 years of age on day of signing informed consent

          -  Recurrent epithelial ovarian/fallopian tube or primary peritoneal cancer (serous,
             clear cell, endometrioid, mixed or poorly differentiated or carcinosarcoma) based on
             imaging or synchronous primary ovarian and uterine cancer patients with any of the
             histology subtypes mentioned above regardless of platinum sensitivity, prior stage or
             number of prior treatment lines

          -  Symptomatic ascites or pleural effusion or both requiring >= 1 drainage within 4-weeks
             of study entry or has a peritoneal/pleural drainage catheter in place to control
             symptoms

          -  Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

          -  Patient has not received bevacizumab or pembrolizumab or other immune checkpoint
             inhibitor treatment for 3 months prior to enrollment

          -  Life expectancy of >= 3 months

          -  Participants of childbearing potential must have a negative urine or serum pregnancy
             within 72 hours prior to receiving the first dose of study medication. If the urine
             test is positive or cannot be confirmed as negative, a serum pregnancy test will be
             required

          -  Participants of childbearing potential must be willing to use 2 methods of birth
             control or be surgically sterile or abstain from heterosexual activity for the course
             of the study through 90 days after the last dose of study medication (participants of
             childbearing potential are those who have not been surgically sterilized or have not
             been free from menses for > 1 year). Should a woman become pregnant or suspect she is
             pregnant while she is participating in this study, she should inform her treating
             physician immediately

          -  Willing and able to self-administer APL-2 (Pegcetacoplan) (administration by caregiver
             will be allowed)

          -  No known absolute contraindication to bevacizumab and/or pembrolizumab treatment per
             enrolling provider

          -  Willing to receive vaccination against Neisseria meningitidis, Streptococcus
             pneumoniae, and Hemophilus influenzae if randomized into an APL-2 (Pegcetacoplan)
             receiving arm, and if not already vaccinated

          -  Participant must understand the investigational nature of this study and sign an
             Independent Ethics Committee/Institutional Review Board approved written informed
             consent form prior to receiving any study related procedure

        Exclusion Criteria:

          -  Is currently receiving any additional cancer therapy or participating or used an
             investigational drug or device within 3 weeks of the first dose of treatment

          -  Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any
             other form of immunosuppressive therapy within 7 days prior to the first dose of trial
             treatment or, is taking any other medication that might affect immune function

          -  Has active autoimmune disease that has required systemic treatment in the past 3
             months (i.e. with use of disease modifying agents, corticosteroids or
             immunosuppressive drugs). Replacement therapy (e.g. thyroxine, insulin, or physiologic
             corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not
             considered a form of systemic treatment

          -  Has an active infection requiring systemic therapy

          -  Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the trial, interfere with the participant's
             participation for the full duration of the trial, or is not in the best interest of
             the patient to participate, in the opinion of the treating investigator

          -  Pregnancy or lactation

          -  Unwilling or unable to follow protocol requirements

          -  Any condition which in the investigator's opinion deems the participant an unsuitable
             candidate to receive study drug