The phrase "more responsibilities on" is correct and can be used in written English.
It is typically used to convey that someone has been given or has taken on additional duties or tasks. Example: After the promotion, Sarah had more responsibilities on her plate, including managing a team and overseeing project deadlines.
"He has to delegate more and put more responsibilities on other people.
In the wake of those scandals, new laws have been passed, loading yet more responsibilities on to their shoulders.
The obvious way would be to put more responsibilities on those capable of work to seek it.
Besides being asked to fill more responsibilities on special teams — he has worked on returning punts and blocking field-goal attempts for the first time — McKnight has been handed an opportunity to fill the retired LaDainian Tomlinson's role.
In what the state calls a realignment of the criminal justice system, the plan places more responsibilities on the counties, and some local officials say they are unprepared and underfinanced to get the job done.
Haddin, 35, who comes over as an old-fashioned, uncomplicated Aussie who has done the rounds, does not look like a man who craves any more responsibilities on this tour.
Democrats in Congress are pushing for a bigger rescue plan, one that puts more responsibility on the lenders that marketed all those ridiculous mortgages.
And to some extent, one might wish for a little more responsibility on the part of our politicians.
The Jets' inability to establish a consistent running game has heaped more responsibility on Sanchez to make plays and has, at times, also minimized one of his strengths — throwing on the move.
The smaller company puts more responsibility on each dancer.
"There is more responsibility on the coach but this is normal.
