Whereas the design and properties of single-output almost optimal five-valued spectra (AOFVS) Boolean functions on Fn2, whose Walsh spectra take the values in {0,±2⌊n/2⌋,±2⌊n/2⌋+1}, have been considered in several works, to the best of our knowledge the design of their vectorial counterpartF: Fn2→ Fm2has not been addressed so far. Based on a special kind of partitioning the vector space Fn2into disjoint linear codes (not all of them having the same dimension), for the first time we were able to specify vectorial AOFVS functionsF: Fn2→ Fn/2+12, for evenn. This has been achieved by identifying certain properties of the dual codes in the partition of Fn2. Moreover, for the first time, we could specify suitable quadruples (f1,...,f4) of AOFVS functions in a generic manner, whose concatenation f =f1||f2||f3||f4is bent. Due to a particular specification of the constituent functionsfi, we could also establish their exclusion from the completed Maiorana-McFarland (M#) class. Lastly, we introduce theD0class of AOFVS functions (similarly to the Carlet’sD0class of bent functions) and specify again suitable quadruples within this class, whose concatenation is provably bent and outside theM#class. Most notably, by doubly modifying functions in the generalized Maiorana-McFarland (GMM) class, we obtain AOFVS quadruples (f1,...,f4) for which we can fully specify the so-calledM-subspaces of eachfi. This allows us to determine their linearity index (the maximal dimension of any subspaceVfor whichDaDbfi= 0, for alla, b∈V), which is shown to be at most two, for any suchfi∈B2k+2andk≥ 3. Consequently, we deduce thatf=f1||f2||f3||f4∉M#, and additionally these bent functions have the lowest possible linearity index in certain cases, so thatDaDbf≢ 0 for any linearly independentaandb.