  Limits on $\beta^+$EC and ECEC processes in $^{112}$Sn and on
$\beta^-\beta^-$ decay of $^{124}$Sn to the excited states of $^{124}$Te have
been obtained using a 380 cm$^3$ HPGe detector and an external source
consisting of natural tin. A limit with 90% C.L. on the $^{112}$Sn half-life of
$0.92\times 10^{20}$ y for the ECEC(0$\nu$) transition to the $0^+_3$ excited
state in $^{112}$Cd (1871.0 keV) has been established. This transition is
discussed in the context of a possible enhancement of the decay rate by several
orders of magnitude given that the ECEC$(0\nu)$ process is nearly degenerate
with an excited state in the daughter nuclide. Prospects for investigating such
a process in future experiments are discussed. The $\beta^-\beta^-$ decay
limits for $^{124}$Sn to the excited states of $^{124}$Te were obtained on the
level of $(0.8-1.2)\times 10^{21}$ y at the 90% C.L.
