Inclusion Criteria:

* Able to provide written informed consent
* Diagnosis of either Non-CLL B cell malignancy or CLL/SLL
* Ineligible for or have exhausted standard therapeutic options and have relapsed or refractory disease
* ECOG performance status 0-2
* Fertile patients must agree to use highly effective contraception during and for 5 months (male patients) and 8 months (female patients) after last dose of XmAb13676
* Able and willing to complete the entire study

Additional Patient Inclusion Criteria for the DLBCL Cohort (Expansion Phase)

1. Histologically confirmed diagnosis (specified by 2016 World Health Organization) of DLBCL or transformed low-grade lymphoma with measurable disease
2. Patient must be refractory or have relapsed after 2 or more standard therapeutic options, at least one of which must have included anti-CD20 antibody therapy.
3. Not a candidate for or refusing treatment with hematopoietic stem cell transplantation

Additional Patient Inclusion Criteria for the Follicular Lymphoma Cohort (Expansion Phase)

1. Diagnosis of follicular lymphoma Grades 1-3a
2. Patient must be ineligible for or have exhausted standard therapeutic options and have had 2 or more prior systemic regimens.

Exclusion Criteria:

* Cytotoxic chemotherapy, radiotherapy, or immunotherapy including other anti-CD20 antibodies within 4 weeks, or small molecule or investigational agents within 6 elimination half-lives of the first dose of XmAb13676
* Prior allogeneic stem cell or solid organ transplantation
* Failure to recover from Grade 3 or 4 toxicity from previous treatment
* Multiple myeloma/plasma cell leukemia or B cell acute lymphoblastic leukemia
* Known intolerance to CD20 monoclonal antibody therapy
* History of primary central nervous system lymphoma or neoplastic central nervous system disease
* Platelet count \< 50 x 10\^9/L
* Absolute neutrophil count \< 1.0 x 10\^9/L
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) at screening \> 3x upper limit of normal (ULN)
* Bilirubin \> 1.5 mg/dL unless prior diagnosis and documentation of ongoing hemolysis or Gilbert's syndrome has been made)
* Estimated creatinine clearance \< 50 40 mL/min
* Active/uncontrolled autoimmune disease
* Clinically significant cardiac/cardiovascular disease, or pulmonary compromise
* Seizure disorder
* History of stroke with the past year6 mos prior to study entry
* History or evidence of a clinically unstable/uncontrollable disorder, condition or disease other than primary malignancy, that in the opinion of the Investigator would pose a risk to the patient safety or interfere with the study evaluation, procedures or completion
* Evidence of any serious bacterial, viral, parasitic or systemic fungal infections within the 30 days prior to study entry
* Positive test for human immunodeficiency virus (HIV) or hepatitis C (HCV) antibodies (unless HCV viral load test by PCR is negative)
* Positive test for HbsAg, or positive test for HBcAb (unless serology is positive due to recent intravenous immunoglobulin therapy). HBcAb positivity will be allowed if HBsAb is present.
* Patient is pregnant or breast feeding, or planning to become pregnant while enrolled in the study, and 8 months after the last dose of study drug
* Positive urine pregnancy test (ie, urine human chorionic gonadotropin) at screening
* Live viral vaccine within 2 weeks of the first dose of XmAb13676