candidates supported by both major parties

As early as the first Federal elections in 1788, there were candidates, who while alligned with one party or another, was supported in the press by both parties in a particular election.

Constitutional Convention

Convention: In Law, A body constituted by statute to represent the people in their primary relations, and in some sense outside of the constitution, as e.g. for the framing or amending of the constitution itself (Constitutional Convention). In this sense, applied to a body meeting under authority of Congress to frame a constitution for a new state, or convened by a state legislature, in the manner prescribed by law, to revise the constitution of the state.

Oxford English Dictionary

Many states during this time period continued to either create (for new states) or refine their state constitutions. This resulted in numerous elections for convention delegates.

1787 - 1824: Alabama, Connecticut, Delaware, Georgia, Illinois, Indiana, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Missouri, New Jersey, New York, Ohio, Pennsylvania, Rhode Island, South Carolina, Tennessee, Vermont, Virginia

Office Scope: State / Territory

Role Scope: State / County / District / City