The phrase "a notch higher" is correct and usable in written English.
You can use this phrase to describe something that is slightly more than the previous level or amount. For example, "The game's difficulty level was upped a notch higher than usual."
The clothes here are a notch higher in price.
The green portion of the EU recovery plan comes in a notch higher than the US plan at 14%.
She describes it as a level of hell a notch higher than the rural life she left at age 14.
The lacrostitute is a notch higher on the social scale than the 'frat slut.' And dammit that's something worth fighting over".
They did not have the power to force this on their governments but, nevertheless, Greenwich's symbolic standing was raised a notch higher in the public consciousness.
Shrimp Veracruz climbed a notch higher on the spice meter, six charred shrimp that had been massaged with red chili sauce and served with the same side dishes.
In bureaucratic rank alone, Mr. Cambone stands a full notch higher than any predecessor, as under secretary of defense for intelligence, a post created by Congress only last year.
Today it still has a AA rating, one notch higher than Japan's.
The ballet pitches that film's tendency to stylised excess one notch higher, as a kind of enraptured surrealism takes over; the music metamorphoses the dancer, a knife becomes a rose, the audience turns into an ocean.
So while Big Bazaar stays focused on serving its customers and gradually upgrading as the customer base matures, Biyani has his eyes peeled on the opportunity on a more premium offering a few notches higher than Big Bazaar.
And these are those that are rated another notch higher, another notch higher.
