Testing a new drug combination for advanced biliary tract cancer

* INCLUSION CRITERIA:
* Participants must have histopathological confirmation of BTC or histopathological confirmation of carcinoma in the setting of clinical and radiological characteristics which, together with the pathology, are highly suggestive of a diagnosis of BTC.
* The maximum tumor size of any individual tumor or metastasis must be \<= 8 cm.
* Participants should have progressed on standard of care first line systemic treatment or refused standard treatment.
* Participants must have a disease that is not amenable to potentially curative resection or liver transplantation.
* Participants must have evaluable or measurable disease per RECIST 1.1
* ECOG performance status of 0 to 1
* Participants must have adequate organ and marrow function as defined below:

Absolute neutrophil count

(ANC) \>= 1,000/mcL

Platelets \>= 100,000/mcL

Total bilirubin \<= 2.5 x ULN

ALT and AST \<= 5 x ULN.

Creatinine OR Measured or calculated creatinine clearance (CrCl) (estimated glomerular filtration rate (eGFR) may also be used in place of CrCl)

\<1.5x institution upper limit of normal OR

\>= 45 mL/min/1.73 m2 for participant with creatinine levels

\>= 1.5 X institutional ULN

* Age \>=18 years.
* Participants must have recovered from any acute toxicity related to prior therapy, including surgery. Toxicity should be \<= grade 1. Note: participants with thyroid dysfunction caused by prior therapy including the need for chronic therapy are eligible.
* Individuals of child-bearing potential (IOCBP) and individuals able to father a child must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) at the study entry, for the duration of study treatment and up to 4 months after the last dose of the CDX-1140 or Keytruda(R) (all individuals), 9 months (IOCBP), 6 months (individuals able to father a child) after completion of CAPOX therapy whatever comes later
* Nursing participants must be willing to discontinue nursing from study treatment initiation through 4 months after study treatment discontinuation.
* HBV-infected participants must be on antivirals and have HBV DNA \<100 IU/mL. HCV-infected participants can be enrolled if HCV RNA level is undetectable.
* Participants must be able to understand and willing to sign a written informed consent document.

EXCLUSION CRITERIA:

* History of a homozygous or compound heterozygous variants in the DPYD gene associated with complete or near complete absence in dihydropyridimidine dehydrogenase (DPD) activity.
* Participants who have had standard-of-care anti-cancer therapy or therapy with investigational agents (e.g., chemotherapy, endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal antibodies, or other investigation agents) or large field radiotherapy within 4 weeks prior to treatment initiation.
* Prior therapy with anti- CD40.
* Receiving of live vaccines within 30 days prior to the treatment initiation. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, Bacillus Calmette-Guerin, and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist(R)) are live attenuated vaccines and are not allowed.
* Major surgery within 4 weeks prior to treatment initiation.
* Active central nervous system metastases and/or carcinomatous meningitis.
* HIV-infected participants.
* History of (non-infectious) pneumonitis or current pneumonitis.
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to study drugs or other agents used in study, such as nivolumab, dacetuzumab, APX005M, ADC-1013.
* Prior invasive malignancies within the past 3 years prior to treatment initiation (with the exception of non-melanoma skin cancers, non-invasive bladder cancer, or localized prostate cancer for whom systemic therapy is not required).
* Any medical condition that requires chronic systemic steroid therapy, or any other form of immunosuppressive medication (inhaled and topical steroids are permitted).
* History of chronic autoimmune disease (e.g., Addison's disease, multiple sclerosis, Graves' disease, Hashimoto's thyroiditis, rheumatoid arthritis, hypophysitis, systemic lupus erythematosus, Wegener's granulomatosis, sarcoidosis syndrome, etc.) or other connective tissue diseases with the symptomatic disease within the 3 years of initiation of study treatment. Note: Active vitiligo or a history of vitiligo will not be a basis for exclusion.
* Fridericia's corrected QT interval (QTcF) \>= 480 msec 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.
* Participants who were not able to tolerate prior immune checkpoint inhibitor therapy.
* Uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements.
* Pregnancy.