  We report the most restrictive direct limits on masses of fourth-generation
down-type quarks $b^{\prime}$, and quark-like composite fermions ($B$ or
$T_{5/3}$), decaying promptly to $t W^{\mp}$. We search for a significant
excess of events with two same-charge leptons ($e$, $\mu$), several hadronic
jets, and missing transverse energy. An analysis of data from $p\overline{p}$
collisions with an integrated luminosity of 2.7 fb$^{-1}$ collected with the
CDF II detector at Fermilab yields no evidence for such a signal, setting mass
limits $m_{b^{\prime}}, m_{B} >$ 338 $\mathrm{GeV}/c^2$ and $m_{T_{5/3}} >$ 365
$\mathrm{GeV}/c^2$ at 95% confidence level.
