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Unfortunately, there is nothing you can do on Business Catalyst to redirect the .aspx pages.

This is what we have done in the past for situations where we needed to make sure the .aspx pages are redirected and you do not have access to existing server. The solution is not ideal, and takes a bunch of extra work, but may be worth it for clients who are really concerned with SEO:

1. Build new website on BC
2. Take the HTML/CSS output of all the pages and load onto another server outside of BC.
3. Setup the redirects for all pages on the site (including the .aspx pages) to the new .html location on this temporary server
4. Point the domain to the temporary server
5. Wait until Google has indexed the new location of the pages
6. Point the DNS over to the BC website

Or, I believe Oleg's suggestion will work if you do this prior to moving the website over to Business Catalyst. Putting redirects on the old server will not do anything if you have pointed the DNS or the a records over to BC already.