J. Maíz Apellániz, R. C. Gamen, G. Holgado, S. Rosu, J. I. Arias, S. Simón-Díaz, A. Pellerin, M. Abdul-Masih, E. Madero Fuentes, J. A. Molina-Calzada, R. H. Barbá

(ABRIDGED BUT NOT TOO FAR) Multiplicity is ubiquitous among massive stars and its understanding is constrained by the sample of well-determined orbits. The immediate goal of M3W is to significantly increase the number of massive multiple systems with well-determined orbits and masses. We will address issues such as multiplicity statistics, the mass function in clusters and the field, the properties of binaries with compact companions and gravitational-wave progenitors, the origin and characteristics of runaways and their 3-D motions, the use of apsidal motion as a probe of stellar interiors, and the mass discrepancy between different methods (evolutionary, spectroscopic, and Keplerian). In this first paper, we present the project; describe the data and tools that will be used, including the disentangling UNWIND tool; analyse the very massive twin binary system GLS 11 448; and briefly introduce some of the following papers of the series. We present a new orbit for GLS 11 448, using UNWIND to obtain for the first time disentangled spectra for the full 3820-11 000 $\mathring{A}$ range for an OB spectroscopic binary. We derive the stellar parameters, making new stellar lines available for the study of O stars. The Aa and Ab components of GLS 11 448, both classified as O3.5 II(f*), are the two most massive O stars ever detected according to the evolutionary masses of 70$\pm$10 M$_\odot$ and 76$\pm$11 M$_\odot$ determined in this paper. We also report the first-ever detection of the interstellar He I 10 830 triplet in absorption in an OB-star sightline. As a by-product of the ISM model derived for UNWIND using GLS 11 448 and five other standard stars, we present the most detailed diffuse-interstellar-band (DIB) library ever built, with a total of 631 DIBs in the 4000-17 100 $\mathring{A}$ range, of which 37 are fitted with multiple-Gaussian profiles and 119 had never been identified before.