Simply be familiar with the known OSes for the 3d metals as shown in the table, very easy to do so once you understand the underlying concept :
(And don't forget that the 3d metals Sc and Zn, are not transition metals).
From Sc to Mn, maximum OS increases from +3 to +7, due to increasing number of 3d electrons available to be lost (in both ionic and covalent compounds), but decreases from +7 to +2 from Mn to Zn, due to the increasing dominance of the opposing factor of increasing nuclear charge (going from left to right of the period), outweighing the previous factor of availability of 3d electrons.
With an additional proton in Fe (compared to Mn) resulting in stronger electrostatic attraction between the valence electrons and the positively charged nucleus, it no longer becomes thermodynamically feasible for Fe to lose 7 electrons (in both ionic and covalent compounds), hence the maximum OS decreases to +6, and so on for next few elements Co, Ni, etc.
You mentioned “outweighing the previous factor of availability of 3d electrons” is availability of 4s electrons considered too?