Is it possible to put JCheckBoxes in JTable cells, which do NOT contain booleans?

I know that a table cell in a JTable automatically gets a Checkbox, if you set its class to Boolean.

However, I have a column in my JTable, which contains integer values. Is it possible to add Checkboxes to those (non-boolean) cells like in my poor drawing here:checkboxes-draft ?

My goal is not to check those columns for true/false values, but rather to select the corresponding table rows and do something with them. I know that I could use a multiple selection interval in my ListSelectionModel instead, but I'd find it much more appealing with checkboxes.

Thanks in advance !