The purpose of this study is to assess the safety and tolerability of MK-3641 (short ragweed [Ambrosia artemisiifolia] extract, SCH 039641, RAGWITEK®) sublingual tablets and MK-7243 (Timothy grass [Phleum pratense] extract, SCH 697243, GRASTEK®) sublingual tablets co-administered in participants 18 through 65 years of age with both ragweed- and grass polled-induced allergic rhinitis, with or without conjunctivitis and with or without asthma. The primary endpoint is the percentage of participants who experience at least one event of local swelling after co-administration of MK-3641 and MK-7243 sublingual tablets.