A search for the doubly charmed baryon Ξcc+ is performed in the Ξc+π−π+ invariant-mass spectrum, where the Ξc+ 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 Ξcc++→ (Ξc+→ pK−π+)π+ decay for different Ξcc+ 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 Ξcc+→Λc+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. [Figure not available: see fulltext.].