Different inputs but able to generate consistent outputs across different SHA engines
In short, this will be not be possible, even if we only use one secure hash function rather than two.  You seem to be describing a sort of dual second-preimage attack where we need to find two inputs that clash over two separate hash functions.
A secure hash function will be resistant to such attacks.  As such for either SHA2 &amp; SHA3, it will not be possible to find another input that makes a desired output.
I believe that even SHA1 is only weak in terms of collision resistance.  See here for further details.