The temperature dependence of the in-plane magnetic penetration depth (lambda(ab)) in an extensively characterized sample of superconducting CaKFe4As4 (T-c similar or equal to 35 K) was investigated using muon-spin rotation (mu SR). A comparison of lambda(-2)(ab) (T) measured by mu SR with the one inferred from angle-resolved photoemission spectroscopy (ARPES) data confirms the presence of multiple gaps at the Fermi level. An agreement between mu SR and ARPES requires the presence of additional bands, which are not resolved by ARPES experiments. These bands are characterized by small superconducting gaps with an average zero-temperature value of Delta(0) = 2.4(2) meV. Our data suggest that in CaKFe4As4 the s(perpendicular to) order parameter symmetry acquires a more sophisticated form by allowing a sign change not only between electron and hole pockets, but also within pockets of similar type.