Spin-gapless semiconductors (SGS) represent a new type of compounds with potential applications in novel spintronic devices. Here, we performed a comprehensive computational and theoretical study of FeCrTiAl, a quaternary Heusler compound that was recently predicted to exhibit nearly SGS properties. Our calculations indicate that this material undergoes several band structure transitions from essentially semimetallic phase at smaller lattice constants to nearly type-II SGS at the ground state, then to nearly type-III SGS and further to nearly type-I SGS, as the lattice parameter is increased. Another interesting feature of FeCrTiAl is that its spin polarization changes sign from negative to positive as the volume of the cell increases. At the largest considered lattice parameters, this compound exhibits nearly 100% spin polarization. The mechanical expansion discussed in this text may be achieved, in principle, either by applying an epitaxial strain in thin-film geometry, or by chemical substitution, for example with non-magnetic element of larger atomic radius. We hope that the presented results may provide guidance for further research on mechanical strain induced manipulation of electronic and magnetic properties of spin-gapless semiconductors.