Q.Unlike the first ionization enthalpy, the second and third ionization enthalpies of the 3d transition metals increase in a fairly regular way across the series. Explain why.

The first ionization enthalpy of the 3d series is irregular because it depends on the particular stability of the specific $d^n$ or $d^ns^1$ configuration left behind -- which is why chromium (already at the stable $3d^5$ before ionization) is anomalously low, and manganese and zinc (reaching or disrupting a stable configuration on ionization) are anomalously high, as developed in an earlier example.

Once the first electron -- normally the single, comparatively loosely bound $4s$ electron (or one of the pair, for atoms with $4s^2$) -- has already been removed, the situation for the second and subsequent ionizations is more uniform. Every further electron removed comes from the $3d$ subshell of an already singly- or doubly-charged cation. Because these removals are all "the same kind" of process (removing a $3d$ electron from a $3d^n$-type ion, for a steadily increasing series of $n$ and steadily increasing positive charge), the energy required rises in a comparatively smooth, monotonic way that tracks the steadily increasing effective nuclear charge across the row, without the sharp, configuration-specific kinks that arise for the very first electron removed (where whether the atom starts at, reaches, or breaks into a half-filled/filled subshell makes a large and idiosyncratic difference).

In short: the first ionization enthalpy is unusually sensitive to which specific electron configuration (out of $4s^1$, $4s^2$, $3d^5$, $3d^{10}$, and combinations) the atom happens to start from or end up at, while the second and third ionization enthalpies are removing electrons from configurations that do not show these same special stabilities, so their trend is governed almost purely by the steadily rising nuclear charge -- and is correspondingly smoother.

Contrast what is being removed at each ionization step (a 4s electron with configuration-specific stability effects for IE1, vs a 3d electron from an already-ionized species for IE2/IE3) to explain why the later ionizations are smoother.

Assuming ALL ionization enthalpies must be irregular just because the first one is; not identifying that it is specifically the 4s-electron removal (and its associated d^5/d^10 stability effects) that causes the first-IE irregularity.