A nonasymptotically free gauge theory with many couplings is shown to exhibit a ``trapping'' mechanism, in the sense that, as soon as one (or more) of the couplings grows large, the rest of the couplings will follow suit. This mechanism can help achieve a nonperturbative ``unification'' of the standard model in the manner of Maiani, Parisi, and Petronzio at relatively ``low'' energies (TeV scales). Two scenarios are given, one of which is just the standard SU(3${)}_{\mathrm{c}}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{\mathrm{L}}$\ifmmode\times\else\texttimes\fi{}U(1${)}_{\mathrm{y}}$ and the other one involves, in addition, technicolor interactions. Predictions for ${\mathrm{sin}}^{2}$${\mathrm{\ensuremath{\theta}}}_{\mathrm{w}}$(${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{F}}$\ensuremath{\simeq}250 GeV) and ${\ensuremath{\alpha}}_{3}$(${\ensuremath{\Lambda}}_{F}$) are presented for both scenarios. Both scenarios make use of SU(2${)}_{\mathrm{L}}$-singlet heavy fermions which carry charge, color (model I), and technicolor (model II). Some experimental implications are also discussed.