The phrase "additional burden of" is correct and usable in written English.
It can be used when discussing extra responsibilities or challenges that someone has to deal with in a particular context.
Example: "The new regulations impose an additional burden of compliance on small businesses, making it harder for them to operate efficiently."
Alternatives: "extra load of" or "further responsibility of".
In addition to the challenges all homeless youths experience, these youths often have the additional burden of rejection not only from their family, but also from society, simply because of their sexual orientation or gender identity.
St George's also carries the additional burden of national notoriety.
What I did not feel was the additional burden of being "in the wrong".
Children carry the additional burden of keeping their parents alive – mothers and fathers regularly report they would kill themselves were it not for their children.
I've been instructed to prepare for my visit by quitting tea and coffee – the Mayr cure is tough enough without the additional burden of caffeine withdrawal.
The accounting firms that provide consulting services face the additional burden of regulatory concerns about their providing advice to their audit clients.
And it makes the civil rights movement look very nearly random, giving those who followed King an additional burden of disillusionment they don't deserve.
In this case, there's the additional burden of absorbing info about the grandparents and necessarily weighty baggage about the historical context.
"Drivers are already being slammed with skyrocketing gas prices, and they can't shoulder the additional burden of paying $2 more a day on tolls".
McDonald lasted an hour, and a little later came John Sebastian, who was not even on the bill and had the additional burden of having just dropped acid.
But a referee who was an N.B.A. player has the additional burden of managing the expectations of former peers.
