The phrase "an additional request for" is correct and usable in written English.
You can use it when you want to specify that you are making another request in addition to previous ones.
Example: "I would like to submit an additional request for the budget report to be expedited."
Alternatives: "a further request for" or "an extra request for".
President {(C1)}Bush{(T1)} has just announced an additional request for funds of $87 billion, and that is before the U.S. tackles North Korea, Iran and Syria.
Students who were authorized for accommodations during fall semester are guaranteed the same accommodations during their subsequent spring semester without having to make an additional request for the accommodation.
Hicks did not respond to an additional request for comment from The Huffington Post.
Glendale Unified's attorneys' made an additional request for a "temporary stay" on the county committee's proceedings on the territory transfer until Glendale Unified's attorneys secure the signatures, according to a letter sent by Glendale Unified's attorneys to Nalini Lasiewicz, a member of Unite LCF.
An additional request for use of Runway 10 was again not understood, because of the misunderstanding of the term "runway in use".
Wilson and his sister, Kalei, 15, complained that no investigation occurred, requests for sponsors were hindered and additional requests for a club were declined.
The administration's budget includes an additional $34.9 billion request for Pell grants.
Meanwhile, after an additional British request for assistance on 6 August 1914, the Australian government hurriedly prepared another expeditionary force to destroy the German wireless stations at Yap in the Caroline Islands, Nauru, and Rabaul in New Britain.
"When he was hundreds of thousands of dollars in debt," Bick allegedly returned to the "modest home" of an "elderly woman" who had invested "to ask for an additional $10,000, a request for funds she declined as she literally did not have the money".
Some states, like California and Michigan, do not require an additional or separate request for an extension.
