This trial will test whether a novel therapeutic approach, cat immunotherapy combined with an investigational new drug called MEDI9929/AMG 157 (an anti-TSLP [thymic stromal lymphopoietin] antibody being co-developed by Amgen and MedImmune) can lead to lasting tolerance to cat allergen.The objective of the study is to determine whether one year of immunotherapy combined with MEDI9929/AMG 157 can induce tolerance to cat allergen.