AMX0035 and Progressive Supranuclear Palsy

Inclusion Criteria: * Male or female 40 to 80 years of age, inclusive * Diagnosis of possible or probable PSP Richardson Syndrome * Presence of PSP symptoms for \<5 years * Score of \<40 on the total (28-item) Progressive Supranuclear Palsy Rating Scale (PSPRS) * Able to walk independently or with minimal assistance * Minimum score of 24 on the Mini Mental State Examination (MMSE) * Must reside outside a skilled nursing facility or dementia care facility at the time of screening. Residence in an assisted living facility is allowed * Must have a study partner willing to attend study visits and provide information on participant's status * Capable of providing informed consent * Capable and willing to comply with trial procedures including visits to the trial clinic, visit requirements and treatment schedule, including MRI scans * Female participants of childbearing potential must agree to use effective birth control for the duration of the study and for 6 months after last dose of study drug. * Males must agree to use effective birth control method for the duration of the study and for 6 months after the last dose of study drug. Men must not plan to donate sperm. Exclusion Criteria: * Require use of a feeding tube * Evidence of any neurological disorder that could explain signs of PSP * Evidence of any clinically significant neurological disorder other than PSP, including significant cerebrovascular abnormalities, vascular dementia, motor neuron disease or ALS, Huntington's disease, normal pressure hydrocephalus, brain tumor, seizure disorder, multiple sclerosis, or known structural brain abnormalities. * History of autosomal dominant PSP due to a Microtubule Associated Protein Tau (MAPT) mutation * History of an autosomal dominant mutation associated with Frontotemporal Lobar Degeneration (FTLD) * Prior or current diagnosis of schizophrenia, schizoaffective disorder, or bipolar disorder * Presence of unstable psychiatric disease, cognitive impairment (e.g., major cognitive dysfunction), dementia, major depression, or substance abuse that would impair ability of the participant to provide informed consent and follow instructions * Abnormal liver function * Renal insufficiency * Ongoing anemia * History of Class III/IV heart failure per New York Heart Association (NYHA)