A public opponent of a bill that would eliminate per-country caps on employment-based green cards is introducing his own legislation to nearly double the amount of employment-based green cards available each year.

The Backlog Elimination, Legal Immigration, and Employment Visa Enhancement (BELIEVE) Act (S. 2091) would increase the total number of green cards available in four of the five employment-based categories, Sen. Rand Paul (R-Ky.) said July 11. Per-country caps also would be eliminated, and the spouses and children of immigrant workers wouldn’t be counted against the visa numbers.

Increasing visas could be a tough haul considering President...