Sustainable intensification of agricultural systems has been suggested as a way to increase food, fiber, energy, and feed to meet future demands. Field pennycress (Tblaspi arvense L.) is proposed as a means for temporal intensification of agriculture, increasing profitability through oilseed production while providing needed cover to address soil and water quality issues. Field research was conducted across four environments in Minnesota to (i) evaluate pennycress planting date and seeding rate on pennycress and soybean [Glycine max (L.) Merr.] seed production and (ii) determine the role of pennycress systems as a weed management tool. Pennycress seeding rate had a direct effect on pennycress yield at Rosemount but not at Waseca or Lamberton locations. The use of a companion cover crop along with pennycress further reduced pennycress seed yield at Rosemount, but not Waseca or Lamberton suggesting that water availability is a key driver in pennycress productivity. The effect of pennycress and cover crops on soybean yield was also dependent on location. At Rosemount, soybean yield was reduced when pennycress was planted ahead of soybeans both years of the study while there was no effect of pennycress on soybean yield at Waseca. Although soybean yield was reduced at Rosemount, the combined pennycress and soybean seed yield was greater. This research shows the potential for a double cropping system of pennycress–soybean to increase overall seed yield and reduce early-season weed pressure.