I have got my hands full already with all kinds of work, and haven't got the time for any more.

我手头已经堆满了各种工作，因此我无暇再搞别的事啦。

《新英汉大辞典》

We cannot accept new orders since we have already got our hands full.

我们不能再接受新订单，因为已经忙得不可开交了。

youdao

In a company, both employers and employees have their hands full with their work, meaning they may not have enough time to skim through your letter's contents.

公司里，雇主和员工都是工作满满的，这就意味着他们也许没足够时间慢慢阅读你的请辞。

youdao

Urban authorities in Britain have their hands full these days chasing explosives, yet some of them seem to have an obsession with a less dangerous substance: chicle.

FORBES: Gobstoppers

In the meantime engineers will have their hands full trying to keep up with the curve.

FORBES: Trick of the Light

In a depressed national job market, headhunters have their hands full filling new technical and business development positions.

FORBES: Why 2013 Will Be a Big Year for NYC's Tech Startups!