<p>I have a poorly designed database. One of the most important tables has 11,000+ entries. We would like to expand our system, and I am wondering if this table grew to 5x its size, would this be a problem? It's 15360 kB in size... if that matters.</p>

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<p>I'm using phpMyAdmin, the server is a Fedora Linux box (nothing fancy), The load is light. It stores just about everything our system uses.</p>

What DBMS? What server? What load? What application?
Besides: 11.000 records are nothing, really. Even in MS Access. :-)
EDIT: 
So I assume you use a fairly recent MySQL with MyISAM tables. In theory, you can go ahead and fill the table into the millions of records. Depending on how you work with them (lots of joins / or not, lots of queries/updates/deletes / or not), you don't need to do anything special. Put a proper index on the table and you should be fine.