Layrisse and co-workers (6, 7, 8, 9) first reported the meat effect on nonheme iron absorption. They observed that veal muscle, veal liver, and fish increased by 150% the nonheme iron absorption in human subjects consuming meals of black beans and maize. Cook and Monsen (10) confirmed these findings in human absorption studies using semisynthetic liquid meals containing glucose, corn oil, minerals, and a protein component. They demonstrated a 2-fold higher nonheme iron absorption from meals containing beef, pork, chicken, and fish as compared with the same meal containing egg albumin. Bjorn-Rasmussen and Hallberg (11) similarly reported that the addition of chicken, beef, or fish to a maize meal increased nonheme iron absorption 2–3-fold compared with no influence with the same quantity of protein added as egg albumin.

It's quite a significant improvement, but from the references the biggest factor appears to be ascorbic acid:

Enhancers of iron absorption are dominated by the effect of ascorbic acid (vitamin C), which can overcome the effects of all dietary inhibitors when it is included in a diet with high non-heme iron availability (usually a meal heavy in vegetables).

Perhaps if you eat a lot of plants and not much meat it might be a decent idea to eat something containing some ascorbic acid with your meal.