It's not possible if they want to be able to over-punch their current stock of 5-bit punched used tapes. Proof: take for instance the character U. U has 4 holes, leaving 3 unpunched spots, which means 7 possibilities for modification (2^3 - 1 = 7). Those 7 possible modified Us must cover all of the 25 non-U letters.

We can assume then that it's not a requirement to be able to over-punch their existing used 5-bit punched stock. Then it's possible, and my proof above of why it's not possible to convert a 4-hole U to more than 7 other characters is a big hint as to one solution... think of a primary encoding and a secondary encoding. What property must the primary encoding have in order to guarantee any character in the primary encoding can be over-punched to one of 25 characters in the secondary encoding?