This paper presents an algorithmic method for solving the two-plant simultaneous bounded domain stabilization problem for SISO LTI systems. This problem has no closed form solution. The solution provides robust performance in the presence of sensor or actuator failure, or other major parameter changes. Vidyasagar (1987) studied a similar problem involving partially bounded stability domains. However, stability with respect to partially bounded domains only partially bound performance characteristics, such as control energy and transient response. The current investigation gives necessary conditions for simultaneous bounded domain stability and demonstrates a geometry-based solution algorithm which can be automated. The possible solutions to the problem and the admissible solutions are represented as sets of points in Euclidean space. The solution to the problem is found by using computational geometric techniques to detect points in the intersection of these two sets, if there is one, and deducing the simultaneous stabilizing compensator design from the points found in the intersection.