The phrase "a further dimension to" is correct and usable in written English.
It can be used when discussing an additional aspect or layer of complexity to a topic or idea.
Example: "The new research adds a further dimension to our understanding of climate change."
Alternatives: "an additional aspect of" or "a new layer to".
There is a further dimension to all this.
This adds a further dimension to the abuse of connections – the control factors in communication.
"Carla's digital expertise, editorial vision and industry profile will add a further dimension to our global operations".
"Bringing U.K. equity distribution into the group adds a further dimension to our U.K. corporate finance business".
Now this one adds a further dimension to understanding the art, design and lifestyles of the country's erstwhile rulers.
Travel, which he loved to share with his wife Cherie, added a further dimension to his writing, and he retained an enthusiasm for steam trains and propeller aircraft.
The ESI-IMS-MS data presented here not only demonstrate an important and informative further dimension to ESI-MS, but also illustrate the potential of the ESI-IMS-MS technique for unravelling protein folding enigmas in general and studying protein misfolding diseases in particular.
These substates add further dimension to the storage of information.
Ginger-like fresh galangal slices and slivers of preserved lime add further dimension to nasi kari ikan.
The resulting crunchy bits will add a further dimension of flavour to the musty, "off" notes that the rind adds (what do you mean, you don't eat the rind?).
With their wide, graphic wigs adding a further dimension of texture to a plastic raincoat or an off-the-shoulder top with a rubbery silk finish, the collection seemed to blend in with the stone floor.
