Ordering scripts stack
Scripts can be stacked. The order is determined by a priority field, but when objects have the same priority, the input order determines the order. Objects specified first are closest to the note. You may also want to override the #'script-priority to give your Script or TextScript overall priority (if you do so, remember to use \once if you don't want the whole score to be affected).
\version "2.24.0"
%% http://lsr.di.unimi.it/LSR/Item?id=255
\relative c'' { c4^"inner up"^"outer up"_"inner down"_"outer down" }