Diboson production in association with jets is studied in the fully leptonic final states, pp → (Z/γ*)(Z/γ*) + jets → 2ℓ2ℓ′ + jets, (ℓ, ℓ′ = e or μ) in proton-proton collisions at a center-of-mass energy of 13 TeV. The data sample corresponds to an integrated luminosity of 138 fb−1 collected with the CMS detector at the LHC. Differential distributions and normalized differential cross sections are measured as a function of jet multiplicity, transverse momentum pT, pseudorapidity η, invariant mass and ∆η of the highest-pT and second-highest-pT jets, and as a function of invariant mass of the four-lepton system for events with various jet multiplicities. These differential cross sections are compared with theoretical predictions that mostly agree with the experimental data. However, in a few regions we observe discrepancies between the predicted and measured values. Further improvement of the predictions is required to describe the ZZ+jets production in the whole phase space.