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We report the observation of multiple magnetic transitions in single crystals of EuPtAs using magnetization, transport, and thermodynamic measurements. EuPtAs crystallizes in the noncentrosymmetric tetragonal LaPtSi-type structure (space group I41md) and undergoes a second-order antiferromagnetic transition at 14.8 K, which is followed by a first-order transition at about 7.5 K. Both transitions are suppressed by magnetic fields applied parallel and perpendicular to the c axis, and multiple field-induced transitions are observed for both field directions, leading to complex temperature-field diagrams with a dome-like magnetic phase for fields parallel to the c axis. Moreover, the dependence of the low temperature resistivity on the application of a training field, but the lack of remanent magnetization, suggests the presence of multiple antiferromagnetic domains in zero-field.