The primary purpose of the study is to understand how well the study drug can eliminate abnormal plasma cells and laboratory signs of high-risk monoclonal gammopathy of undetermined significance (HR-MGUS) and non high-risk smoldering multiple myeloma (NHR-SMM). This requires understanding the safety and tolerability of the study drug (how the body reacts to linvoseltamab) as well as the effectiveness of the study drug (how well linvoseltamab eliminates plasma cells). All participants will start treatment with gradually increasing doses of linvoseltamab (step-up doses) before they start receiving the assigned full dose. The study is split into 2 parts: * In Part 1, separate groups of 3-6 patients will receive different full doses of linvoseltamab to evaluate the short-term side effects (safety) and tolerability of the study drug within the first 5 weeks after starting treatment. The data collected will help to make a decision about the dosing regimens chosen for Part 2. * In Part 2, a larger number of participants will be randomized to different dosing regimens to further assess the side effects of linvoseltamab, and to evaluate the ability of linvoseltamab to eliminate abnormal plasma cells in HR-MGUS and NHR-SMM. The study is looking at several other research questions, including: * How many participants treated with linvoseltamab have improvement of their HR-MGUS or NHR-SMM? * What side effects may happen from taking the study drug? * How much study drug is in the blood at different times? * Whether the body makes antibodies against the study drug (which could make the drug less effective or could lead to side effects).