Can I use a 1031 Exchange AND a self funded retirement to acquire new property?

[Jeffrey A DeAngelis]

Had a house bought and sold as part of a Self Funded Retirement account. Money is sitting there waiting. 

Have another house about to close that is self funded outside of the Retirement account. 

If I 1031C exchange the self funded house (Titled to my personal name) identify and a new property, have the $$ sit in an intermediary, can I also use the Self Funded Retirement Trust account to purchase new property along with the 1031C exchange?

I assume this will cause complications with how they title the new property.