Magento

We have a client who owns a sign company that we are moving to Magento.  His current site has thousands of products, many with multiple attributes that are displayed based on the type of sign selected and the type of material selected.  Some products can have up to 5 attributes.  The current website is http://www.signstoyou.com.  Sign 1 could have 10 material options and 3 additional attributes all of which are triggered by the type of sign selected.  Sign 2 could have 10 material options and 4 additional attributes, all of which are again triggered by the type of sign selected and so on.

We need to be able to re-create this functionality within Magento but have yet to find a way to do it.