  A search for the $\it{\Xi}^{++}_{cc}$ baryon through the $\it{\Xi}^{++}_{cc}
\rightarrow D^{+} p K^{-} \pi^{+}$ decay is performed with a data sample
corresponding to an integrated luminosity of 1.7 $\mathrm{fb}^{-1}$ recorded by
the LHCb experiment in $pp$ collisions at a centre-of-mass energy of 13 TeV. No
significant signal is observed in the mass range from the kinematic threshold
of the decay to 3800 $\mathrm{MeV}/c^{2}$. An upper limit is set on the ratio
of branching fractions $\mathcal{R} = \frac{\mathcal{B}(\it{\Xi}^{++}_{cc}
\rightarrow D^{+} p K^{-} \pi^{+})}{\mathcal{B}(\it{\Xi}^{++}_{cc} \rightarrow
\Lambda^{+}_{c} K^{-} \pi^{+}\pi^{+})}$ with $\mathcal{R} < 1.7 \hspace{2pt}
(2.1) \times 10^{-2}$ at the 90% (95%) confidence level at the known mass of
the $\it{\Xi}^{++}_{cc}$ state.
