Escalating Doses of Memantine in Down Syndrome (MEDS-123)

Inclusion Criteria: * Cytogenetically documented Trisomy 21 or Complete Unbalanced Translocation of Chromosome 21. Mosaic Trisomy 21 and partial translocations will be excluded from the study. * Vital signs within normal limits for age. * No pregnancy by serum testing at screening. Females of child-bearing potential, sexually active must be practicing a reliable method of birth control. Urine pregnancy tests will be done at the 2 follow-up medical visits. * Laboratory findings within normal limits or judged clinically insignificant at baseline. * Vital signs within normal limits for age. Stable, medically treated hypotension will be allowed. * ECG must demonstrate predominately normal sinus rhythm. Minor abnormalities documented as clinically insignificant will be allowed. * Participants and their authorized representatives will provide written informed consent. * Participants who have received any experimental drug for DS must undergo a washout for a minimum of 5 half-lives of any experimental medications. * All participants must: Be in general good health as judged by the investigators; Be able to swallow oral medication; Have a reliable caregiver or family member who agrees to accompany participant to all visits, provide information about the participant as required by the protocol, and ensure compliance with the medication schedule; Be sufficiently proficient in English to reliably complete the study assessments Exclusion Criteria: * Participant weighing less than 40 kg * Current psychiatric or neurologic diagnosis other than Down syndrome (This includes, but is not limited to, major depressive disorder, schizophrenia, schizoaffective disorder, any other psychotic disorder, bipolar disorder, seizure disorder (no seizures for more than 3 years), autism, Down syndrome regression disorder, Alzheimer disease, Parkinson's disease, cerebrovascular disease, other dementias, brain tumor, or other known structural brain abnormalities.) * Current treatment with psychotropic drugs. * Drug or alcohol abuse or dependence within past 5 years. * Significant suicide risk or who would require treatment with electro-convulsive therapy or with psychotropic drugs during the study or who have received treatment with a depot neuroleptic drug within 6 months of entering the study. * Current or expected (within the next 6 months) hospitalization or residence in a skilled nursing facility (may reside in group homes or other residential settings with no skilled nursing). * Active or clinically significant conditions affecting absorption, distribution, or metabolism of study drug (e.g. inflammatory bowel disease or celiac disease) * Significant allergies to or other significant intolerance of memantine therapy, its ingredients, or with contraindications to memantine therapy as stated in the prescribing information. * Use of NMDA receptor antagonists, such as amantadine (Symmetrel), ketamine, or dextromethorphan during the 30 days prior to screening. * Participants who are expected to require general anesthetics during the course of the study. * Presence or recent history of seizure disorder (\< 3 years). * Clinically significant and/or clinically unstable systemic disease. (Those with controlled hypothyroidism must be on a stable dose of medication for at least 3 months prior to screening and have normal serum T-4 and TSH at screening; and those with controlled diabetes mellitus must have an HbA1c of \< 8.0% and a random serum glucose value of \< 170 mg/dl). * Severe infections or a major surgical operation within 3 months prior to screening. * Unexplained alkaline urine conditions. * Participants with severe renal impairment (i.e., estimated glomerular filtration rate \[eGFR\] \< 30 mL/min/1.73m2) will be excluded from the proposed clinical trial. The eGFR will be calculated using the eGFR Calculator from the National Kidney Foundation (https://www.kidney.org/professionals/gfr\_calculator) using serum creatinine, age, sex, adjusted for body surface area (for medication-related decision making, using Dubois Method). * Participants with severe hepatic impairment (Child-Pugh Category C) will also be excluded from the proposed clinical trial. Child-Pugh Category will be calculated using the MSD Professional Version online calculator (https://www.msdmanuals.com/professional/multimedia/clinical-calculator/child-pugh-classification-for-severity-of-liver-disease). * History of persistent cognitive deficits immediately following head trauma. (Note: remote history of head trauma without cognitive sequelae is not an exclusion.) * Cardiac QTc interval ≥ 480 ms. * History or presence of encephalitis. * Donation of blood or blood products less that 30 days prior to screening, while participating in the study, or four weeks after completion of the study * Inability to comply with the protocol or perform the outcomes measures due to significant hearing (\>40 dB hearing loss) or visual impairment (best corrected visual acuity of less than 20/60) or other clinically relevant issues, such as behavioral issues that may prevent full participation in the study.