Ferromagnetic shape memory Alloys such as off-stoichiomentric Ni₂FeGa have much larger ductility than classical Ni-Mn-Ga alloys due to the presence of the γ-phase. The attractive mechanical properties of these alloys open up the possibility of their implementation into novel actuators or sensors. Properties of these alloys are very sensitive to the slight variations of composition and addition of quaternary elements such as cobalt. We show that Co addition in alloy with composition of Ni₅₄Fe_20-xCo_xGa₂₆ results in a large variety of transformation behaviors. We found that an increase of x from 0 to 9 at. % leads  to (i) a linear change of martensitic transformation temperature from -70^oC to 120^oC; (ii) a non-monotonous change of the Curie temperature from 25^oC for x=0 to a maximum of 100^oC for x=6at.%, and (iii) a linear decrease of saturation magnetization from 60 to 43 emu/g. Despite difficulties in reproducing the same phase content in powder samples, the powder x-ray diffraction patterns seem to demonstrate a crystal structure evolution from modulated crystal lattices to non-modulated lattices with increasing x. The temperature behaviors of the elastic modulus and internal friction in DMA measurements are found to be similar to Ni-Mn-Ga alloys. Up to 6% of superelastic strains are obtained in the tension mode for the non-oriented single crystalline alloy with x=6at.%. The magnetostrain measurements show a training effect which is a clear evidence for magnetic-field-induced twin-boundary motion.