We have measured the magnetization of UCu_5-xPd_x (x = 0.7, 1, 1.5, 2) in fields H as large as 30 T and for temperatures between 1.4 K and 150 K. A composition- and temperature-dependent characteristic field {H}*({x},{T}) is identified, which separates two different non-Fermi liquid scaling regimes, present even in zero field. For {H}≥{H}*({x},{T}), composition-independent scaling is found, while for {H}≤{H}*({x},{T}), different exponents are found for each composition. This second phase is centred in temperature and composition around the x = 1,T = 0 critical point, and we argue that it is consistent with the presence of a Griffiths phase.