A search for the doubly charmed baryon $\Xi cc+$ is performed in the $\Xi c+\pi -\pi +$ invariant-mass spectrum, where the $\Xi c+$ baryon is reconstructed in the $pK-\pi +$ final state. The study uses proton-proton collision data collected with the LHCb detector at a centre-of-mass energy of 13$\mathrm{Te}V$, corresponding to a total integrated luminosity of 5.4$\mathrm{fb}-1$. No significant signal is observed in the invariant-mass range of 3.4$-$3.8$\mathrm{,Ge\kern -0.1em V}/c^2$. Upper limits are set on the ratio of branching fractions multiplied by the production cross-section with respect to the $\Xi cc++\to (\Xi c+\to pK-\pi +)\pi +$ decay for different $\Xi cc+$ mass and lifetime hypotheses in the rapidity range from 2.0 to 4.5 and the transverse momentum range from 2.5 to 25$\mathrm{Ge}V/c$. The results from this search are combined with a previously published search for the $\Xi cc+\to \Lambda c+K-\pi +$ decay mode, yielding a maximum local significance of 4.0 standard deviations around the mass of 3620$\mathrm{Me}V/c2$, including systematic uncertainties. Taking into account the look-elsewhere effect in the 3.5$-$3.7$\mathrm{,Ge\kern -0.1em V}/c^2$ mass window, the combined global significance is 2.9 standard deviations including systematic uncertainties.