Immune Modulation During Palynziq® Treatment in Adults (IMPALA)

The overall objective of the study is to evaluate the ability of MTX, when co-administered with Palynziq, to suppress immune responses to Palynziq and thus improve the tolerability and efficacy of Palynziq in adults with phenylketonuria (PKU). Up to 12 participants will be enrolled into the study across 2 cohorts, with a target enrollment of 6 participants into each cohort: * Cohort A: Individuals with uncontrolled blood phenylalanine (Phe) \> 600 μmol/L on existing management who have never been treated with Palynziq (Palynziq naïve) * Cohort B: Individuals who have uncontrolled blood Phe \> 600 μmol/L after ≥ 24 consecutive weeks of treatment with Palynziq, are on a current dose of≥ 20mg/day, and are unable to further dose escalate (Palynziq experienced) Palynziq will be initiated (Cohort A) or will continue (Cohort B) as indicated in the Palynziq United States Prescribing Information (USPI) and as prescribed by the participant's treating physician. The decision to initiate or continue Palynziq must be made independently of participation in this study. Palynziq and MTX will not be supplied by BioMarin as part of participation in this study. All participants will be administered MTX at an oral dose of 15 mg/week concurrent with Palynziq: * Cohort A participants will have a 4-week Screening Period, followed by a 4-week MTX Tolerability Period during which only MTX will be administered. If MTX is tolerated during the MTX Tolerability Period, the participant will then enter the 24-week Combination Treatment Period during which MTX + Palynziq will be administered concurrently. * Cohort B participants will have a 4-week Screening Period. Participants will then have 24 weeks of concurrent MTX + Palynziq treatment (Combination Treatment Period): participants will be assessed for MTX tolerability during the first 4 weeks of MTX + Palynziq (MTX Tolerability Period) and then receive another 20 weeks of MTX + Palynziq. After completion of Week 24 (Combination Treatment Period), MTX will be discontinued for both cohorts and Palynziq only will continue for another 24 weeks (to Week 49; Follow-up Period). Participants will be assessed for safety and MTX tolerability. If a participant in either Cohort A or B is unable to tolerate MTX, the participant will be discontinued from MTX treatment. Participants who discontinue from MTX early should continue to complete the remaining study assessments until as long as such continued participation will not detrimentally affect the health, safety, and welfare of the participant per investigator determination