This will never happen.
First the request was made by the EuroChamber of Commerce, not the Foreign Affairs office on behalf of the government.
Second, the Schengen area have very specific requirements that every country that applies for visa removal have to comply. The Dominican Republic complies with none of them, specially on the area regarding percentage of immigration violations committed by its citizens.
Having traveled extensively around the world with a Dominican passport I can say is a real burden having to get visas from every other country, but at the same time is better that those visas are required so the harm done by people form this country traveling around and dragging our citizens reputation to the ground is limited to the places that they can get visas to.
I started thinking this way after seeing first hand what happened in Argentina, a country that was opened for Dominicans before and got closed (visa required) recently due to the bad behavior of certain Dominicans, now even when holding a visa a Dominican passport invokes extra careful check at Argentina border control posts.