This work is an extension of the recent spinor-connection theory of Szekeres, Cullinan, and Lynch. In that theory, a geometric model for the gravitational and electromagnetic fields was realized by use of both left- and right-connection groups acting on a 4\ifmmode\times\else\texttimes\fi{}4 spinor tetrad. Here the right-connection group is enlarged in a natural way from a one-parameter to a three-parameter Lie group. This enlargement introduces two extra potential fields which may provide a simple model for the strong and weak fields in curved space-time. A solution to the new field equations is given for a neutral ``pionlike'' particle exhibiting the strong and gravitational fields.