The phrase "at a higher volume" is correct and usable in written English.
It can be used when referring to an increase in sound level, such as in music, speech, or any audio context.
Example: "Please play the music at a higher volume so everyone can enjoy it."
Alternatives: "at an increased volume" or "at a louder level".
"He doesn't come around as much," said Jeter, who knew Steinbrenner at a higher volume.
It's also played in movie theaters at a higher volume than it's ever been.
Printed at a higher volume than the hardback, it usually sells in greater numbers, but at lower margins.
It is as if the same song is being played in a different key, at a higher volume, though its melody remains constant.
"The sound is a lot more pronounced because it can vibrate at a higher volume without breaking," Mr. Nickerson said, standing near a bust of Benjamin Franklin.
You have themes that open up and then disappear only to be picked up at another level, but at a higher volume.
Bossie spoke first, at length and at a high volume, enunciating syllables by pounding the air with his hands.
When the results are not up to DeGuglielmo's standards, the linemen are sure to hear about it — at a high volume.
He could often be heard talking loudly on the telephone in Arabic in the mornings, and in the afternoon he streamed Arabic television stations at a high volume.
Like many poets in the modern tradition, she relies on charged words and phrases to create an atmosphere of portent and high emotion rather than attending to precision or sense; she writes vaguely but at a high volume.
Schilling may be a more complete pitcher, but he still plays at a high volume, and his fastball was clocked at 97 miles an hour in the ninth inning of Game 5 of the division series against the St . Louis Cardinals
