  Searches for top quark-associated physics such as $t\bar t W$ or $t\bar t H$
in final states with multiple leptons require a careful accounting of expected
backgrounds due to the lack of reconstructible resonances. We demonstrate that
the rare top quark decays $t \to \ell' \nu b \ell\ell$ and $t \to q q' b
\ell\ell$, when a soft lepton is not detected, can contribute a non-negligible
background to such searches. Simulations in the LHC experiments typically do
not account for such decays and as such backgrounds to such searches may be
underestimated.
