More intense/risky than "bleeding-edge":
Leading-edge: Implies being at the absolute forefront, even ahead of the bleeding edge. Often used in technology and scientific fields.
Frontier: Evokes a sense of exploration and pushing into uncharted territory.
Experimental: Highlights the untested nature of the innovation.
Similar to "cutting-edge" but less common:
State-of-the-art: Emphasizes the use of the most advanced techniques and technologies currently available.
Avant-garde: Suggests a more artistic or unconventional approach to innovation.
Groundbreaking: Highlights the transformative potential of the innovation.
Focusing on specific aspects:
Competitive edge: Refers to an advantage that a company has over its rivals.
Strategic edge: Emphasizes the long-term benefits of the innovation.
Technological edge: Specifically highlights advancements in technology.
The best "edge" to use will depend on the specific context and the nuance you want to convey.