Splitting Staff into two

[Yoshiaki Onishi]

> Is there any possibility of doing something like this picture below? On top 
> is lilypond's default output and on the bottom is what I seek to write.
> 

Dear Lucas,

Referring to the following pages on LilyPond Documentation:

https://lilypond.org/doc/v2.23/Documentation/notation/modifying-single-staves 
https://lilypond.org/doc/v2.25/Documentation/notation/ossia-staves 
https://lilypond.org/doc/v2.25/Documentation/notation/clef 
https://lilypond.org/doc/v2.23/Documentation/notation/flexible-vertical-spacing-within-systems
 

The following is my attempt in replicating what you have proposed. The trick, 
it seems, is to redefine where the Middle C position is going to be after the 
staff change takes place, as well as overriding the staff spacing. For the 
latter, resorting to setting via Scheme code seems to be the trick. 

\version "2.24.4"

\new Staff = "main" {c''1 d'' e'' f'' 

\stopStaff
  \override Staff.StaffSymbol.line-positions = #'(-9 -7 -5 -3 -1)
  \set Staff.middleCPosition = -11
\startStaff
 <<
    { c''1 d'' e'' f''  }

    \new Staff \with {
      \remove Time_signature_engraver
      alignAboveContext = "main"
      \magnifyStaff #2/3
  \override VerticalAxisGroup.default-staff-staff-spacing =
    #'((basic-distance . 0)
       (minimum-distance . 0)
       (padding . -1)
       (stretchability . 10))
      firstClef = ##f
    }
    { c''1 d'' e'' f'' }
  >>
}

I hope this gets close to what you want to accomplish!

All the best,
Yoshi