No way to differentiate Select widgets with the same parameters? (Id would be a good update to widgets?)

There is a Select widget displayed in multiple tabs in my app. All the parameters of the widgets are the same because it serves the same purpose in all the tabs. They are contained in different objects, though (because they are in different tabs) so I can’t get their value with a single callback method. I tried to circumvent this by modifying the size and differentiating the widgets based on their size in a single callback method:

TypeError: Constant parameter 'size' cannot be modified

It would have been a somewhat unsatisfactory solution anyway: the widget size would have changed while the user would have surfed the tabs. All the Select widgets are created by a sinlge function and there is no clever way of differentiating their size while they are being created. Would an id - which could also be modified after the widget has been initialised - as a widget parameter be a good idea to implement in Panel?