I have come back simply put they don't have legal authority for an intermediate codeshare - These are rather rare animals as they require 6th and 7th freedoms in addition to 5th Freedom treaty conditions.
EU-US openskys allows EU and US carriers to operate from any point between treaty states but not for domestic sectors. Any flight shall be by aircraft registered in signatory states- Look at Norwegians issues.
Singapore and the US have similar openskys.
However the MAN-IAH sector meets none of these conditions.
The flight may well gain a codeshare IAH- SIN at some point however UA still won't be able to market the IAH-MAN-IAH as a codeshare any time soon.
The only thing UA can expect is feed from Singapore ticket holders to the selected and authorised SQ codeshare points - Atlanta, Austin, Dallas, Fort Lauderdale, Orlando (in addition to the VS codeshare), Miami, New Orleans, and Tampa where Singapore has code authority.
Beyond that it simple interline arrangements.
BTW they can't codeshare on the intermediate FRA-NYC sector either.