Dawn visits both Vesta and Ceres, thanks to its patient solar electric ion propulsion. AFAIK more xenon and perhaps a little more hydrazine for the attitude thrusters, would've sufficed to give it power to visit even more targets.
But what is the geography of a multi asteroid trip like? Looking at the diagrams below, asteroid families are identified with similar semi-major axis, inclination and eccentricity. Could a SEP spacecraft like Dawn+ visit several asteroids a year within such a family? Massalia and Koronis look pretty well concentrated. And aren't most NEA thought to come from one single family with low inclination in the inner part of the Main Belt and wouldn't it be interesting and easier to visit them out there than trying to catch them at perihelion where they are more spread out due to differences in eccentricities and higher velocities?
Couldn't Dawn make even one single near passage of any other asteroid during its long trip from Vesta to Ceres? Several other spacecrafts, like Rosetta and Chang'e 3 (upper stage) and New Horizons have done asteroid flybys without even being Main Belt missions.
To understand the scale in these diagrams, 0.1 AU is about 250 times the distance Earth-Moon. The distance between the perihelion Dwarf-Ceres is 0.5 AU which is about the distance between Earth and Mars when at the closest. The inclination of the Moon is about 1.5 degrees.
Inclination and semi-major axis: Inclination and eccentricity: