I agree with Star Strider's advice to scale the data. That will still result in y-ticks for each YRuler. Here are two alternatives, both of which use undocumented methods tested in r2021a but may not work in future releases.
Demo 1: remove ytick for all YRulers except the first
Remove the yticks for all YRulers except the one on the far left. If the YRulers have different scales this will be misleading unless you document the scales somehwere on the figure.
data = rand(100,5).*[1 1e-06 1e-08 1e08 1e10];
origState = warning('query', 'MATLAB:structOnObject');
cleanup = onCleanup(@()warning(origState));
warning('off','MATLAB:structOnObject')
set(S.YRulers(3:end), 'TickLabels', '')
See addendum below for an additional required step!
Before and after:
Demo 2: change exponent notation
data = rand(100,5).*[1 1e-06 1e-08 1e08 1e10];
origState = warning('query', 'MATLAB:structOnObject');
cleanup = onCleanup(@()warning(origState));
warning('off','MATLAB:structOnObject')
set(S.YRulers(n+1), 'TickLabelMode', 'auto', 'Exponent', -3)
set(S.YRulers(n+1), 'TickLabelMode', 'auto', 'TickLabelFormat', '%.3f')
See addendum below for an additional required step!
Addendum: prevent auto restoration of ticks
The changes above will be lost as soon as the axes are changed in any way (e.g. resize figure). To prevent the restoration of the original ticks, disable the MarkedClean listener. This should all go toward the end of your plotting code and I haven't explored what else this may effect!!
listener with properties:
Source: {[1×1 ParallelCoordinatesPlot]}
Callback: @(~,~)markedCleanCallback(pc)
S.AutoListeners__{1}.Enabled = false;