set Matlab WindowButtonDownFcn and preserve default behavior

can I manually set WindowButtonDownFcn and selectively overwrite the right or middle-click, while preserving default behavior? Ultimate goal would be to copy figure to clipboard on some click.

set(gcf,'WindowButtonDownFcn',@(src,~) disp(src.SelectionType)); %this seemingly always overwrites default behavior of figure click

I tried this with following error msgs (scroll right)

listener(gcf,'WindowButtonDownFcn',@(src,~) disp(src.SelectionType)) %Event 'WindowButtonDownFcn' is not defined for class 'matlab.ui.Figure'.
listener(get(gcf,'parent'),'WindowButtonDownFcn',@(src,~) disp(src.SelectionType)) %Event 'WindowButtonDownFcn' is not defined for class 'matlab.ui.Root'
handle(gcf).addlistener(handle(gcf),'WindowButtonDownFcn',@(src,~) disp(src.SelectionType)) %Unrecognized method, property, or field 'addlistener' for class 'matlab.ui.Figure'.

and several more permutation using handle and event.listener with no success

Tested in Matlab 2019a.

EDIT: here's a template function to use with modifiers based on matlabgui's kind answer

%copies figure to clipboard when [control]+[right-click] anywhere on figure window (and leaving default functionality intact)
figure; plot(randi(100,1,100)) %random figure
addlistener ( gcf, 'WindowMousePress', @(src,~) myFavFunc(src,[]))

function myFavFunc(src,~)
if strcmp(src.SelectionType,'alt') && numel(src.CurrentModifier)==1 &&  strcmp(src.CurrentModifier,'control')
    print -clipboard -dmeta
    disp('copied figure to clipboard')
end
end

I dont know why Matlab hide some of the events for figures, you can get a list here:

  hFig = figure;
  mc = metaclass(hFig);
  disp ( {mc.EventList.Name}' ) ;

From that info you can then add a listener to the mouse press event:

hFig = figure;
addlistener ( hFig, 'WindowMousePress', @(src,~)disp('myCallback' ))

That will leave the standard figure callback alone, instead of the disp command get it to run a function where you look at the figure property SelectionType to determine which mouse button was pressed. You could extend it to use the CurrentModifier property to determine if Ctrl, Shift or Alt was pressed to further customise it.