yes, you could preserve and possibly increase your rankings.
First, Index your valuable resources ( content, urls, metadata, keyword rankings, etc) that have to be preserved.
If you use Joomla content management system & sh404SEF, you may rewrite URLs and keep them the same as on the current site.
Here is an example of site recently migrated without losing its rankings:
http://www.alaskaflyfishinggoods.com/new-flies-for-2011/view-all-products.html