Sampling of Scenarios (SOS) is just drawing random sets of competitors and random specifications of the firm's product, and summarizing the WTP across those 100s or 1000s of scenarios.
The fundamental WTP calculation is based on simulating the firm's product vs. a set of competitors. Then, writing down that simulated share of preference for the firm's product. Then, enhancing the firm's product and finding the increase in price that drives the share for the firm back to the original share amount prior to enhancing the product.
Details about the approach may be found in this white paper: https://sawtoothsoftware.com/resources/technical-papers/estimating-willingness-to-pay-in-conjoint-analysis
As shown in the white paper, with the assumption of more competitors, WTP decreases somewhat. But, depending on the CBC dataset and attribute list dimensions, the WTP tends to stabilize after about 5, 10, or 20 competitors are assumed. Again, it just depends on the attribute list and the data set. I think with more levels within an attribute, it will take more competitors under the Sampling of Scenarios until WTP stops decreasing. We show two examples in the appendix of the paper I cite above related to this issue.