I have created custom search buttons for myself. You can see below what it looks like
I added a sub menu array to scp/tickets.php The php code is shown below. I was not able to create this based on assigned user or team but maybe this will help you do that./*Projects*/{$nav->addSubMenu(array('desc'=>__('Pro'), 'title'=>__('Pro'), 'href'=>'tickets.php?sort=status&order=DESC&a=search&t=&query=project', 'iconclass'=>'Ticket'), (!$_REQUEST));}/*END Projects*/