One variable would be for lets say all post within the last 7 days or so
search.php?do=getnew&days=7
One Variable that acts like the search.php?do=getnew
search.php?do=getnew
One that acts like the search.php?do=getdaily
search.php?do=getdaily
One that looks like search.php?do=QOTW that only pulls from my QOTW forums
search.php?do=getnew&forumid=QOTWid
To make the URLs nicer, you could use a Plugin on Hook search_start to set the necessary Variables inside search.php to hide it form the User, eg. define new do-actions like lastweek, etc.
If you want a completely new file for it - just copy search.php