The phrase "a somewhat deeper" is correct and usable in written English.
It can be used when describing a level of depth that is greater than a certain baseline but not excessively so.
Example: "The analysis provided a somewhat deeper understanding of the underlying issues at play."
Alternatives: "a slightly greater" or "a moderately deeper".
Try talking slower and in a somewhat deeper voice.
Disagree with them I might and do, but I finished this book with a somewhat deeper appreciation for them than before.
Within hours, negotiators appeared to have the outlines of a possible deal, with a smaller pay cut than in the rejected package, a somewhat deeper set of benefit cuts, and the elimination of job guarantees.
The idealized female profile of Venus de Milo demonstrates a somewhat deeper mentolabial angle of 95°.
The neutral plane is likely at a comparable but somewhat deeper depth.
"My has always been somewhat deeper, with a heavy bass and my moody vein," he says.
It's not a simple case of "you had to be there," as any contemporary assessment of director Yu Suzuki's Shenmue series to date (two commercially released games proper, a canned MMO and a smartphone title that bombed without reaching the West) goes somewhat deeper than that surface-scraping assessment of the situation.
A preview sample of the Dehesa paleta was somewhat deeper in color than the 5 Jotas, but was also nut-sweet, satin-textured and mellow.
Now a new Internet service allows ordinary citizens with somewhat deeper than ordinary pockets to commission custom portraits from eminent biographers like Judith Thurman, Francine du Plessix Gray and Diane Wood Middlebrook.
The swing bowler Bhuvneshwar Kumar is also recovering from a hamstring injury but India's reservoir of pacemen is somewhat deeper than that of Bangladesh.
Nickel carbide disappeared at 723 K in the most surface-sensitive spectra recorded at 150 eV kinetic energy, while a small amount of carbide is still present in the somewhat deeper near-surface layers.
