Inclusion Criteria:  Subject must be ≥ 18 or ≥ 16 years of age with a minimum body weight of 50 kg.  Subject must have a diagnosis of SS, defined by the presence of the SS18-SSX rearrangement, as confirmed by the Investigator (evidence from the diagnostic pathology of prior biopsy must be available). Subject must have advanced SS, which for the purposes of this study, is defined as any of the following:  Metastatic Local (primary or recurrent), unresectable (with Investigator and Medical Monitor approval)  Subject must have been treated with ≤ 4 regimens of systemic chemotherapies. Subjects who have undergone > 4 regimens of systemic chemotherapy may be permitted with Medical Monitor approval. Subjects must have:  Demonstrated progression of disease on their most recent therapy or Discontinued their most recent therapy due to the potential for cumulative toxicity, intolerability or lack of continued clinical benefit, in the opinion of the Investigator.  Eligible subjects with progression of disease on their most recent therapy may enroll in the Dose Escalation Phase and in Arm 1 of the Dose Expansion Phase. Eligible subjects with responsive and/or stable disease on their most recent therapy may enroll in the Dose Escalation Phase and in Arm 2 of the Dose Expansion Phase.  Note: Inclusion criterion 15 provides timing requirements for prior therapy.  Subject must have measurable disease by RECIST v1.1, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with calipers and/or CT scan. Measurable lesions cannot have undergone any local treatment or radiation nor can any local treatment or radiation involving measurable lesions be anticipated. Subject or his/her parent or legal guardian (when applicable) must be able to understand and be willing to sign an informed consent and, when applicable, subject must sign assent form. Subject must be willing and able to comply with scheduled study visits and treatment plans. Subject must be willing to undergo all study procedures (biopsies at baseline, at least 1 on-treatment and at EOT [unless contraindicated due to medical risk; other exceptions to this are at the discretion of the Sponsor's Medical Monitor]), laboratory testing, and imaging approximately every 8 (or 12) weeks independent of dose delays, interruptions, and/or reductions.  Subject must have an ECOG PS of ≤ 2.  • Arm 2 (Dose Expansion Phase): Subject must have an ECOG PS of ≤ 3  Subject must have a life expectancy of ≥ 3 months.  • Arm 2 (Dose Expansion Phase): Subject must have a life expectancy of ≥ 2 months  Subject must have adequate venous access for IV drug administration and blood collection.  Subject must have adequate cardiac function as evidenced by:  LVEF of ≥ 40% by ECHO. Other methods of evaluating LVEF may be performed according to institutional practice. Corrected QT interval (QTc) using Fridericia's formula (QTcF) < 470 msec  Subject must have adequate hepatic function as evidenced by:  Serum total bilirubin ≤ 1.5 × upper limit of normal (ULN) (≤ 3.0 × ULN for subjects with Gilbert's syndrome) Aspartate aminotransferase (AST), alanine aminotransferase (ALT) ≤ 3.0 × ULN (≤ 5.0 × ULN if liver metastases are present) Alkaline phosphatase (ALP) ≤ 3.0 × ULN (≤ 5.0 × ULN if liver metastases are present and/or known bone disease is present) No known portal vein thrombosis  Subject must have adequate renal function as evidenced by:  • Glomerular filtration rate (GFR) ≥ 50 mL/min (based on a contemporary, widely accepted, and clinically applicable equation that estimates glomerular filtration rate or a measure of glomerular filtration rate (e.g. Chronic Kidney Disease Epidemiology Collaboration CKD-EPI)  Subject must have adequate hematologic function as evidenced by:  Hemoglobin ≥ 8 g/dL (Red blood cell [RBC] transfusions to achieve this level will be permitted up to 7 days prior to start of study drug and complete blood count [CBC] criteria for eligibility are confirmed within 24 hours of first study dose.) White blood cells (WBCs) ≥ 2.0 × 109/L Absolute neutrophil count (ANC) ≥ 1.0 × 109/L Platelets > 50 × 109/L (Transfusions to achieve this level will be allowed up to 72 hours prior to start of study drug.)  Subject must have adequate coagulation function as evidenced by:  • International normalized ratio (INR) ≤ 1.5 or prothrombin time (PT) ≤ 1.5 × ULN and partial thromboplastin time (PTT) ≤ 1.5 × ULN if not receiving anticoagulation therapy.  Note: For subjects on anticoagulants, exceptions to these parameters are allowed if they are within the intended or expected range for their therapeutic use. Participants must have no history of clinically significant active bleeding (within 14 days of first dose of study drug) or pathological condition that carries high risk of bleeding (for example, tumor involving major vessels or known esophageal varices).  Timing requirements with respect to prior therapy and surgery are as follows:  At least 2 weeks or at least 5 half-lives, whichever is shorter, must have elapsed since administration of the last dose of any prior anticancer therapy (including investigational agents). 4 weeks must have elapsed since the last major surgery, laparoscopic procedure, or significant traumatic injury. Note: Central line placement, subcutaneous port placement, core biopsy, fine needle aspiration, and bone marrow biopsy/aspiration are not considered major surgeries. 2 weeks must have elapsed since the last radiotherapy. Palliative radiation therapy is allowed so long as it does not involve the target lesion(s). Toxicity related to prior therapy must have returned to ≤ Grade 1 by CTCAE at least 14 days prior to study start. Exceptions include Grade 2 alopecia and other Grade 2 toxicities determined to be stable and irreversible by the Investigator with approval of the Medical Monitor.  Female subjects must be:  Postmenopausal, defined as at least 12 months post-cessation of menses (without an alternative medical cause); or Permanently sterile following documented hysterectomy, bilateral salpingectomy, bilateral oophorectomy, or tubal ligation or having a male partner with vasectomy or having a female partner as affirmed by the subject; or Nonpregnant, nonlactating, and if sexually active having agreed to use a highly effective method of contraception (ie, hormonal contraceptives associated with inhibition of ovulation or intrauterine device [IUD], or intrauterine hormone-releasing system [IUS], or sexual abstinence) from Screening Visit until 90 days after final dose of study drug. Male subjects must have documented vasectomy or if sexually active must agree to use a highly effective method of contraception with their partners of childbearing potential (ie, hormonal contraceptives associated with the inhibition of ovulation or IUD, or IUS, or sexual abstinence) from Screening until 90 days after final dose of study drug. Male subjects must agree to refrain from donating sperm during this time period.  Exclusion Criteria:  Subject (or his/her parent or legal guardian, when applicable) is unable to provide informed consent (or assent, when applicable) and/or to follow protocol requirements. Subject has other malignancy which may interfere with the diagnosis and/or treatment of SS and/or interpretation of outcome results. Subject has an active severe infection requiring systemic therapy. Subject is permitted to enroll once any required antibiotic and/or antifungal therapy has been completed and/or infection is determined to be controlled. Subject has active hepatitis B virus (HBV) or hepatitis C virus (HCV) infections; subjects with a sustained viral response to HCV treatment or immunity to prior HBV infection will be permitted. Subject has known positive human immunodeficiency virus (HIV) antibody results or acquired immunodeficiency syndrome (AIDS)-related illness; subjects with CD4+ T-cell counts ≥ 350 cells/µL will be permitted, as will subjects who have not had an AIDS-related illness within the past 12 months. Subject has an uncontrolled concurrent medical disease and/or psychiatric illness/social situation that in the opinion of the Investigator could cause unacceptable safety risks or compromise compliance with the protocol. Subject is receiving systemic steroid therapy for acute illness (stable doses for controlled chronic disease are permitted) or any other systemic immunosuppressive medication. Local steroid therapies (inhaled or topical steroids) are acceptable. See Exclusion criterion 7 for details on steroids in the setting of central nervous system (CNS) disease.  Subjects with known CNS metastases are only permitted under the following conditions: Brain metastases must have been stable for the at least 2 months since completion of most recent CNS-directed intervention. Subject may be on corticosteroids so long as the dose is stable or decreasing at the time of study entry. Anti-epileptic therapy is allowed so long as medications are not otherwise excluded and seizures have been controlled for at least 4 weeks since the last anti-epileptic medication adjustment. Subjects with active brain metastases and/or leptomeningeal disease are excluded.  Dose Escalation Phase: Subjects with known CNS metastases that meet the above conditions are permitted to enroll in dose escalation. Arm 1 (Dose Expansion Phase): Subjects with known or suspected CNS metastases are excluded from Arm 1. Arm 2 (Dose Expansion Phase): Subjects with CNS metastases that meet the above conditions are permitted to enroll in Arm 2. Subject has known hypersensitivities to components of FHD-609. Subject has prior exposure to a BRD9 degrader. Subject is participating in any other clinical trials. Exceptions include participation in any observational or nontherapeutic clinical trials.