Today we got some dynamic simulation of what happens if Neptune's orbit is nudged by 1/1000. 0.0000515 M☉ at 30.07 AU semimajor, 29.81 AU peri'. So they're looking to nudge its peri' 0.03 AU, I guess.
The main candidate is Gliese (GJ) 710. This is a 0.6 M☉ mass coming within 14000 AU some say 10k. We'd have to look first at what Neptune's orbit might evolve into after 1.29 million Earth years which is 7827 2/3 Neptune's. Keeping also in mind that we don't know if Planet Nine exists.
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