Is consecutive multiple transformation of Y variable a valid approach statistically?
Combining analytical transformations (say $f$ and $g$), as you suggest, is nothing else than applying a single $u = f\circ g$ transformation, so it is as valid as applying any simple transformation.

You just need to make sure that the transformation works (in this case, $y&gt;0$ in the whole dataset and in the predictions, so that $\sqrt{log(y+1)}$ is real), and of course that it remains invertible, i.e. the initial variable can be retrieved from the transformed value, without ambiguity (this requires the transformation to be injective).

The transformation you suggest seems valid. You could also try a second log-transformation instead of the square root.