Unfortunately, the answer to your question is simply "No, it is not possible with current HTML and Javascript controls"
However, if you use jQuery and this plugin (https://github.com/fnagel/jquery-ui/wiki/Selectmenu) to select a menu, which I suppose you can do:
$("#idofSelect").selectmenu("open");
Another alternative to your idea, but maybe not so fantastic:
document.getElementById("idOfSelect").setAttribute("size", 5);
What this does is just make it multiline, so somehow it displays the parameters ... You can do this in focus, and then do another event when you click, where you reset its size is 1, and stop the event from spreading (so that onfocus is not called after ..) but, as I said, it is TEM professional, so either live with your choice as it is, or switch to jQuery, select the menu and enjoy opening and closing them dynamically as you wish :)
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