The goal of this study is to identify the best way to treat pulmonary embolism (blood clots in the lungs), specifically when there is a large amount of clot, but the patient’s blood pressure is stable. All patients with pulmonary embolism are treated with blood thinner medicines (anticoagulation). Sometimes, doctors will also perform a procedure using a catheter to either remove the clot or give clot-dissolving medicines (catheter-directed therapy). It is not clear whether these procedures help patients who have a large amount of clot but are more stable and at lower risk. This study compares blood thinners alone to blood thinners plus catheter-directed therapy to determine which is more effective. Both treatment approaches are considered standard care for patients with pulmonary embolism who are stable but who have large amounts of clot. The clot-dissolving medicine and devices used in catheter-directed therapy are approved by the U.S. Food and Drug Administration (FDA) for treatment of pulmonary embolism. Participants will be randomly assigned to 1 of 2 groups. Group A will be treated with standard blood thinners and will have catheter-directed therapy to deliver a blood clot-dissolving medicine directly into the blood clot and/or suck out the blood clot. Group B will be treated with standard blood thinners alone.