An increase in the supply of the front-month settlement MBS is not a factor that causes dollar rolls to trade 'special.' The concept of a dollar roll trading 'special' is rooted in the difference in the purchasing rate for the back-month settlement MBS. This situation arises when an investor can acquire the back-month settlement MBS at an implied repo rate that is lower than the rate in the repurchase market. Therefore, any factors that elevate the front-month settlement price and reduce the back-month settlement price are contributors to a dollar roll trading 'special.' However, an increase in the supply of the front-month settlement MBS would lead to a decrease in the price of the front-month settlement MBS, which contradicts the conditions for a dollar roll to trade 'special.' Hence, Choice C is not a factor that causes dollar rolls to trade 'special.'

Choice A is incorrect. An increase in the number of settlement transactions for the back-month date by the originators of the MBS can contribute to a dollar roll trading 'special'. This is because an increase in settlements implies that there are more securities available for trade, which can lead to a decrease in their price and hence a lower implied financing rate.

Choice B is incorrect. An increase in the price of MBS for front-month settlement does not make dollar roll trade 'special'. In fact, it contributes to making it special as higher prices imply lower yields or financing rates, which makes them attractive compared to prevailing market rates.

Choice D is incorrect. A shortage of MBSs in the market for delivery in front-month also contributes to making dollar roll trade 'special'. When there's a shortage, demand exceeds supply leading to higher prices and thus lower implied repo rates than repurchase market rate.