As the offshore industry moves to deeper waters, riser collision becomes a more crucial concern. Riser interference assessments need to rely on time domain simulations due to nonlinearities such as hydrodynamic interferences, however, one difficulty is that riser collision is an extreme event. In a recent work, the authors proposed an efficient procedure for predicting the probability of riser collision, based on extrapolating the dynamic response characteristics; thus obviating the need to capture actual collisions during simulation. However, the prior work considers randomness only from the irregular waves. This paper extends the prior work by developing a method to account for multiple uncertainties. The random variables considered herein are the current, drag coefficient, vessel motions, and riser mass. The proposed method is computationally efficient; the additional simulations necessary to incorporate four random variables are only slightly more than the original simulation case. Using a top-tensioned riser system as a case study, the likelihood of collision predicted by the proposed method is found to compare well with the Monte Carlo simulation. Moreover, it is shown that the random variables can increase the probability by an order of magnitude and all of the considered variables meaningfully contribute to this increase.