Federal libertarians, state republicrats
There is a way in which libertarians' and republicrats' goals can overlap, which can be applied to the benefit of both. That can be done via the following method:
Libertarian candidates for federal legislative offices can agree to not override the legislative actions of the individual states, but only reduce interference on private entities by the federal government. This would ultimately be beneficial to both of the republicratic parties on the state level, because the federal government imposes particular left-wing and right-wing policies that apply to people in both left-wing and right-wing states alike. Thus, with decreased federal laws, taxes, and spending, individual states would be free to become more left-wing or right-wing if they so desire, and individual states would likewise be free to become more libertarian.
Libertarian candidates for federal legislative offices can agree to not override the legislative actions of the individual states, but only reduce interference on private entities by the federal government. This would ultimately be beneficial to both of the republicratic parties on the state level, because the federal government imposes particular left-wing and right-wing policies that apply to people in both left-wing and right-wing states alike. Thus, with decreased federal laws, taxes, and spending, individual states would be free to become more left-wing or right-wing if they so desire, and individual states would likewise be free to become more libertarian.