I think your best option for this would be to first craft one of the DataAssist Search server behaivor. Once it is crafted you can create another or duplicate the first one.
After crafting the search server behaviors you can use a radio group or have a checkbox to specify weather to use the ANDs or ORs. You can then go back to the results page and alter the triggers for the search server behaviors. For the first one you will add in a check for the value of the checkbox to see if it is set to the value specified in the value attribute of the checkbox.
For the second search on the page you will check to see if the posted checkbox does not have the value specified. These custom triggers might look like this:
if(isset($_POST['check1']) && $_POST['check1'] == 'the value'){
the other search trigger
if( (isset($_POST['check1']) && $_POST['check1'] != 'the value') || !(isset($_POST['check1'])) || $_POST['check1'] != 'the value'){
This should give you both searches and one will be used over the other depending on the user selection.
