A search for the doubly charmed baryon Ξ+ccΞcc+ is performed in the Ξ+cπ−π+Ξc+π−π+ invariant-mass spectrum, where the Ξ+cΞc+ baryon is reconstructed in the pK−π+ final state. The study uses proton-proton collision data collected with the LHCb detector at a centre- of-mass energy of 13 TeV, corresponding to a total integrated luminosity of 5.4 fb−1. No significant signal is observed in the invariant-mass range of 3.4–3.8 GeV/c2. Upper limits are set on the ratio of branching fractions multiplied by the production cross-section with respect to the Ξ++ccΞcc++ → (Ξ+cΞc+ → pK−π+)π+ decay for different Ξ+ccΞcc+ mass and lifetime hypotheses in the rapidity range from 2.0 to 4.5 and the transverse momentum range from 2.5 to 25 GeV/c. The results from this search are combined with a previously published search for the Ξ+ccΞcc+ → Λ+cΛc+K−π+ decay mode, yielding a maximum local significance of 4.0 standard deviations around the mass of 3620 MeV/c2, including systematic uncertainties. Taking into account the look-elsewhere effect in the 3.5–3.7 GeV/c2 mass window, the combined global significance is 2.9 standard deviations including systematic uncertainties.