Any effect that is conditional on the state and thermodynamically irreversible counts as a measurement.

One way to do a partial measurement is to make the conditional effects less orthogonal to each other, e.g. cause a target qubit to conditionally rotate by 22 degrees instead of a full 180 degrees.

Another possible concept for a partial measurement is not distinguishing between all of the cases. For example, if a system can be in the x=-1, x=0, or x=1 cases then it's possible to do a measurement that distinguishes x=-1 from x in {0,1} without collapsing all the way down to x=0 or x=1.