[adventured]

New Horizons can and may do exactly that.

http://pluto.jhuapl.edu/Mission/2019-Onward.php

"Future New Horizons extended missions, if funded by NASA, could explore even farther out. The spacecraft is on an escape trajectory from the Sun, traveling about three astronomical units per year. Moreover, New Horizons and its payload sensors are healthy and operating perfectly. The spacecraft has enough power and fuel to operate into the mid-2030s or longer, perhaps enough to reach the boundary of interstellar space."

[RosanaAnaDana]

Yeah but what do you even do out there with the sensor payload it has? Its imaging devices really aren't structured for deep space remote sensing. They were built to image planet and planet sized objects.