Yes. The uniform elogation can be increased maintaining the same UTS by increasing the strain hardening exponent (n). The strain hardening exponent is a function of microstructure. One of the ways to increase the n value if increase in grain size in a single phase material. Of course, there can be other ways also. So depending upon the application can the constrained on has to find ways to increase the n value.

I agree with B. Sarkar. In order to increase the uniform elongation, the begin of necking has to be "postponed" to higher strains. Following the Consider criterium, the key is to increase the strain hardening rate, especially at higher strains. Very effective are effects like the TRIP and the TWIP effect. 

Beside the TWIP and TRIP,  the goal is reached with the so called Q&P steels (just google the abbreviation).

Dear Vindor Kumar,

I agree with Sarkara, Pong and Zisman. The resistance to necking (or in other words, increased uniform elongation) in uniaxial tension is a manifestation of the enhanced work-hardening capacity. Work hardening capacity increases with increasing grain size. It is true; however, we know that large grain size impairs strength and toughness of steel simultaneously. It is for this reason that another mechanism is usually employed to increase work-hardening capacity. The mechanism is introducing a mechanically unstable phase into the microstructure, which transforms to a harder phase under stress. The best example is austenite, which undergoes stress or strain-induced martensitic transformation under tensile testing. However, in this case, in order to increase work-hardening capacity and, therefore, uniform elongation, retained austenite should be at right content and morphology, i.e. > 10 percent and film-like morphology.