Nice playing man!!!
With a great tone you should be able to do as SkinnyViking said. Just double track it and treat it as a rythm track. Although the track you posted more like a solo-melody kind of stuff and then it should be treated more like a solo guitar of course. Some amps can sound both amazingly for rythm and solo guitar so there is no need to change the amp for the different parts of the song. Amps that would work Peavey JSX or the Mesa Mark series, both sound very modern and can get you to smooth solo heaven

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And if the player would like for his solo's to really stick out from the rythm playing i would recommend to switch guitar with totally different pickups then changing amp. That could make allot more difference with this type of playing.