The phrase "overload with" is correct and usable in written English.
You could use it to indicate that something has been assigned with too much or too many tasks or responsibilities. Example: The new intern was overloaded with work, which made them feel overwhelmed and unprepared for the job.
"Administrative overload with increased sanctions may indeed be why there are problems with the statistics.
For some listeners there's a danger of mysticism overload with Ms. Coltrane's music.
More importantly, it could effectively manage data overload with the overload-handling mechanisms.
Days before France's presidential election, the country has gone into talk overload, with both serious debates and silly posturing.
We investigated whether objective measurement of fluid overload with bioimpedance spectroscopy is helpful in optimizing fluid status.
In discussing information overload with Fortune 500 leaders, top scientists, writers, students, and small business owners, email comes up again and again as a problem.
The quintessential kids' dessert is presented with all the pomp and ceremony usually reserved for the Triple Chocolate Overload with Banyuls.
"I believed that the future was going to be marked by a marketing and sales overload with businesses trying to get people to buy their product.
Like Mr. Drain (a possible influence), Mr. Samson tempers the tendency toward visual overload with an interest in making sly points about display and cultural otherness.
The retardation effect of the overload with different stress ratio and overload ratio are quantified by retardation length and cycles.
In aged female rats, ICH induced long-term perihematomal iron overload with upregulated iron handling proteins, neuroinflammation, brain atrophy, neuronal loss and neurological deficits.
