offsetPositions =
#(define-music-function (offsets) (number-pair?)
  #{
     \once \override Slur.control-points =
       #(lambda (grob)
          (match-let ((((_ . y1) _ _ (_ . y2))
                       (ly:slur::calc-control-points grob))
                      ((off1 . off2) offsets))
            (set! (ly:grob-property grob 'positions)
                  (cons (+ y1 off1) (+ y2 off2)))
            (ly:slur::calc-control-points grob)))
  #})

\relative c'' {
  c4(^"default" c, d2)
  \offsetPositions #'(0 . 1)
  c'4(^"(0 . 1)" c, d2)
  \offsetPositions #'(0 . 2)
  c'4(^"(0 . 2)" c, d2)
  \bar "||"
  g4(^"default" a d'2)
  \offsetPositions #'(1 . 0)
  g,,4(^"(1 . 0)" a d'2)
  \offsetPositions #'(2 . 0)
  g,,4(^"(2 . 0)" a d'2)
}