Here's a line of critical thought launched by Samir Okasha. It suggests that the underdetermination thesis derives some of its support from a false assumption that the concepts of empirical equivalence and underdetermination are interchangeable :
It is obviously true that at any given stage of a scientific enquiry the avail-
able data will in principle be compatible with many different, mutually incompatible mpatible theories. This is because theories always outstrip the data on
which they are based, if only by universal generalization - the inference
from data to theory is always deductively invalid. This point is sometimes
expressed by saying that scientific theories are inductively underdetermined by
the data.
Inductive underdetermination is not what most philosophers of science
have in mind when they discuss the underdetermination of theory by data.
In recent discussions, 'underdetermination' usually refers to the idea that
there may be theories between which no possible evidence can decide, not
merely no actual evidence. If two theories are underdetermined in this
stronger sense, then however much empirical data we collect in the future,
we shall never be able to decide between them on empirical grounds. I use
the term 'strong underdetermination' to refer to situations of this sort.
Where I use the term 'underdetermination' without qualification, it refers to
strong underdetermination, not inductive underdetermination.
Why should it be thought that scientific theories are typically, or indeed
ever, strongly underdetermined by data? Many philosophers believe this
because they think that for any scientific theory there always exists an alter-
native empirically equivalent rival theory. Empirically equivalent theories
are those whose empirical or testable implications are identical. Some
authors treat the concepts of empirical equivalence and underdetermination
as interchangeable, but I do not follow their lead. If two theories T1 and T2
are incompatible but empirically equivalent, I see that as a possible reason for
thinking them strongly underdetermined; but the former state of affairs is
not identical with the latter. The rationale for driving a wedge between 'T1
and T2 are empirically equivalent' and 'No possible evidence can decide
between T1 and T2' will become apparent. (Samir Okasha, 'Underdetermination, Holism and the Theory/Data Distinction', The Philosophical Quarterly (1950-), Vol. 52, No. 208 (Jul., 2002), pp. 303-319 : 303-4.)