There have been numerous approaches that have been proposed to enlarge the impedance range of haptic interaction while maintaining stability. However, enhancing the rate-hardness of haptic interaction while maintaining stability is still a challenging issue. The actual perceived rate-hardness has been much lower than what the users expect to feel. In this paper, we propose the successive force augmentation (SFA) approach, which increases the impedance range by adding a feed-forward force offset to the state-dependent feedback force rendered using a low stiffness value. This allows the proposed approach to display stiffness of up to 10 N/mm with Phantom Premium 1.5. It was possible to further enhance the rate-hardness by using the original value of virtual environment stiffness for feedback force calculation during the transient response followed by normal SFA. Experimental evaluation for multi-DoF virtual environment exhibited a much higher displayed stiffness and rate-hardness compared to conventional approaches. Two user studies revealed that the increase of rate-hardness due to SFA allowed the participants to have a faster reaction time to an unexpected collision with a virtual wall and accurately discriminate between four virtual walls of different stiffness.