Mepolizumab in Episodic Angioedema With Eosinophilia

* INCLUSION CRITERIA: A subject will be eligible for participation in the study only if all of the following criteria apply: 1. The subject is male or female, aged 18 years or older. 2. The subject has a documented diagnosis of EAE. 3. The subject has symptoms of EAE in the cycle prior to screening, including but not limited to fever, swelling, hives or rashes, weight gain, muscle pain, and lymphadenopathy. 4. Cycling of eosinophils is ongoing as indicated by a peak absolute eosinophil count (AEC) greater than or equal to 1500/mm\^3 during at least one cycle in the prior 3 months. 5. If taking corticosteroids, the subject is able and willing to stay on a stable dose for 6 weeks prior to screening. 6. The subject agrees to storage of study samples. 7. The subject is able to provide informed consent. 8. Females are eligible for this study if they are: * of non-childbearing potential (i.e., women who have had a hysterectomy or tubal ligation or are postmenopausal as defined by no menses in 1 year); OR * of childbearing potential but willing to practice effective contraception or abstinence during administration of the study drug and for 100 days (5 terminal half-lives) after administration of the study drug. * Not breastfeeding. Participation of Women: Pregnancy: The effects of mepolizumab on the developing human fetus are unknown. For this reason, women of childbearing potential must agree to use adequate contraception (see below for acceptable methods) prior to study entry, for the duration of study participation, and for \>5 terminal half-lives (approximately 100 days) after administration of the last dose of study drug. Nonreproductive potential is defined as post-menopausal, male partner who has azoospermia or is surgically sterile (at least 6 weeks before screening) and is the sole sexual partner, surgical sterility, or a congenital or acquired condition that definitely prevents conception. Further, postmenopausal is defined as at least 12 consecutive months with no menses at age 50 or older, or a high follicle-stimulating hormone level in the postmenopausal range at ages 45-50 years in subjects not using hormonal contraception or hormone replacement therapy. Females with reproductive potential must either practice complete and uninterrupted abstinence from heterosexual activity or use 2 of the following methods of contraception with their partners. The 2 methods must include either 2 barrier methods, or 1 barrier method and 1 non-barrier method, both of which must be consistently used: Barrier Methods: 1. Diaphragm with spermicide 2. Cervical cap with spermicide or contraceptive sponge (for nulliparous subjects only) 3. Male or female condom (cannot be used together) Non-Barrier Methods 1. An intrauterine device with a documented failure rate of \<1% 2. Hormonal contraception: pill (estrogen/progestin or progestin-only), patch, vaginal ring, rod implanted in the skin, or subcutaneous injection methods Females of childbearing-potential must have a negative pregnancy test result prior to receiving mepolizumab at each on-site study visit. During the course of the study, if a woman becomes pregnant or suspects she is pregnant, she should inform the study staff and her primary care physician immediately. A pregnancy registry has been created for subjects who become pregnant while receiving the approved dose of mepolizumab (100 mg subcutaneous injection) for asthma. Fertility: There is no fertility data in humans. Animal studies showed no adverse effects of anti-IL-5 treatment on fertility. EXCLUSION CRITERIA: A subject will not be eligible to participate in the study if any of the following conditions are fulfilled at the time of screening: 1. Treatment with immunosuppressive or immunomodulatory agents including but not limited to cyclosporine, interferon-alpha, azathioprine, methotrexate, and cyclophosphamide within the past 3 months. 2. Treatment with biologics including but not limited to mepolizumab, IVIG, anti-TNF agents, rituximab, benralizumab, alemtuzumab, reslizumab, dupilumab, lebrikizumab, and omalizumab within 6 months or 5 half-lives (whichever is longer). Subjects who received rituximab at any time in the past must have normal B-cell numbers to participate. 3. Co-morbid illness, alcohol or substance abuse, or any other condition (e.g., HIV, active hepatitis) that, in the opinion of the investigator, places the subject at undue risk by participating in the study. 4. Treatment with a daily dose of corticosteroids \>40 mg. Co-enrollment Guidelines: Co-enrollment in other trials is restricted, other than enrollment on observational studies or those evaluating the use of a licensed medication. Study staff should be notified of co-enrollment as it may require the approval of the investigator.