That wouldn't be a problem.
Just insert some kind of switch in the ubbt.inc.php that checks a url param.
So simply create a new directory in "templates" and put your second set of templates there.
There's a variable called $tempstyle that defines the directory from which the templates are read from. The default value is "default".
Have a look at your ubbt.inc.php, find the line:
$tempstyle = "default";
Change it to something like
if ($myurlparam == "style2") {
$tempstyle = "nameOfNewDirectory";
}
else {
$tempstyle = "default";
}