More Opportunities for Rural Economies from DOT Grants Act or the MORE DOT Grants Act This bill revises the process for awarding grants to high-density public land counties and any units of tribal or local governments within such counties under certain Department of Transportation (DOT) programs. Examples of qualifying grant programs include the Infrastructure for Rebuilding America (INFRA) grant program and the Airport Improvement Program (AIP). A high-density public land county is a county that has a population of not more than 100,000 people and in which the federal government owns or manages more than 50% of the land. For these jurisdictions, any requirement for local matching funds under a qualifying grant program must be reduced by 50%. On request, DOT must provide additional technical assistance to such jurisdictions before and during the annual application period for each qualifying grant program. DOT must also prioritize grant applications from such jurisdictions that have not received support under the qualifying grant program during the 10-year period preceding the date of the application. In approving applications for a qualifying grant program, DOT must give special consideration to an application from a high-density public land county or unit of local government within such a county with respect to any rural-set aside designated for the program. DOT may give special consideration to an application from a tribal government within such a county.