  A search for the doubly charmed baryon $\it{\Xi}_{cc}^{+}$ is performed in
the $\it{\Xi}_{c}^{+} \pi^{-} \pi^{+}$ invariant-mass spectrum, where the
$\it{\Xi}_{c}^{+}$ baryon is reconstructed in the $p K^{-} \pi^{+}$ final
state. The study uses proton-proton collision data collected with the LHCb
detector at a centre-of-mass energy of 13$\mathrm{\,Te\kern -0.1em V}$,
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 $\it{\Xi}_{cc}^{++} \rightarrow (\it{\Xi}_{c}^{+} \rightarrow p K^{-}
\pi^{+}) \pi^{+}$ decay for different $\it{\Xi}_{cc}^{+}$ mass and lifetime
hypotheses in the rapidity range from 2.0 to 4.5 and the transverse momentum
range from 2.5 to 25$\mathrm{\,Ge\kern -0.1em V}/c$. The results from this
search are combined with a previously published search for the
$\it{\Xi}_{cc}^{+} \rightarrow \it{\Lambda}_{c}^{+} K^{-} \pi^{+}$ decay mode,
yielding a maximum local significance of 4.0 standard deviations around the
mass of 3620$\mathrm{\,Me\kern -0.1em V}/c^2$, 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.
