MulTags-SARwv is a meticulously curated dataset comprising 2100 synthetic aperture radar (SAR) images acquired by the Sentinel-1 (S-1) satellite s wave mode (WV) at a 36° incidence angle. These images were randomly selected between January and June from 2016-2019 and span an 8° by 8° box centered on the Northwest Tropical Atlantic Station (NTAS) buoy (51°W, 15°N). Each image covers a 20 km by 20 km area with a 5 m pixel resolution. The dataset is the result of visual interpretation and tagging by five experts using 12 defined tags. These tags describe various marine atmospheric boundary layer (MABL) processes near Barbados, including the transition between roll vortices and convective cells, as well as localized phenomena such as fronts, rain events, cold pools, and low winds. Unlike the previous TenGeoP-SARwv dataset, MulTags-SARwv utilizes a multiple tagging strategy to provide a comprehensive description of the MABL processes visible on these WV SAR images. The dataset is organized into a folder (pngs) that includes all 2100 SAR images in PNG format, a text file (tagsInfo.txt) documenting all the assigned tags for each image by the five experts, and a readme.txt file that provides an overall description of the dataset. MulTags-SARwv has significant potential for investigating MABL processes and complements SAR classification materials for the development of machine learning methods.