With the development and wide applications of wireless communication technology, the limited spectrum resources and the fixed spectrum allocation policy could no longer satisfy the demand for wireless communication. Just for this reason, many spectrum resources become spectrum holes because they are allocated but not used. Cognitive radio is now becoming one of the most important techniques for high utility of these spectrum holes. If the holes available to cognitive users are abundant over a certain time, it is a worth consideration to increase network throughputs by orthogonal multiplexing as many as spectrum holes. A multi-transceiver configuration is one of the possible solutions for this purpose. With such a schema, all transceivers within a cognitive user work in a concurrent or parallel mode, by which the throughput of the network can be increased. However, co-site working cognitive radios may incur electromagnetic interference between each other. When more cognitive radios are equipped, much electromagnetic interference may be incurred. Many techniques are proposed to mitigate such so-siting interference; however, none of them have addressed the probability that the interference will happen. If the probability could be estimated in advance, the user will make a better planning on the configurations of the co-siting working radios. Based on an elaborated n-fold multiple integral model, we propose a novel method to decide how many cognitive radios can be installed for one cognitive user at most. This is our main contribution with this work, providing an enhanced ability to determine the optimal number of cognitive radios installed within each cognitive user. We make a strict deduction on electromagnetic compatibility probability with various parameters of cognitive radios. Simulations are performed and the results show that the electromagnetic compatibility of the simulated cognitive radio system meets the deducted probability by this method very well.