What is the farthest likely distance to a companion star to the Sun?

Alpha Centauri and the Sun are about of equal mass and are 4.3 light years apart. The farthest distance for a companion star is probably near 1 light year, but the problem is that the typical random velocity of stars near the solar neighborhod is about a few kilometers/sec and this is the escape velocity from the Sun at a distance of 900 AU or 22 times the distance to Pluto. This is only 0.01 light years, so my guess is that any companion star would be lost from the solar system if it were further away than this distance. We can easily detect such a companion star by its gravitational influence upon Pluto, and we know there is no dwarf star or neutron star this close.