Access (order) overlapping markups in a system

[Urs Liska]

In this sample:

\version "2.19.48"

{
  c2 ^\markup "First markup"
  c2 ^\markup "Second markup"
  c2 ^\markup "Third markup"
}

The markups are starting at the staff and when overlapping are printed
above the preceding one.

Is there a way to have this behaviour reversed so that  they are
starting at the top and go to the bottom?

I know how to achive the attached result with overriding
outside-staff-priority, but is there an automatic way that works line by
line? Or something that can be built with reasonable effort?

Urs

markup-stack.png
Description: PNG image