Weighted Survey Data Comparison of Many Group Means

We have a state representative sample of student data that must be analyzed using survey weights. What I am struggling with, conceptually, is what comparisons are actually possible under this design. We have a categorical variable indicating student 'disability' (physical or behavioral, learning, both physical/behavioral and learning, or no disability) and we have 50+ performance marks for each of the students.

Using Stata, we can run something like svy: tabulate SCORE1 STATUS, wald column it shows there is a difference between the 4 groups of students, but that is all it says. The essence of the report objective though is to show which of the groups are different from which others. Surely something more than the Wald test can be done here.

It is hard to tell which statistical tests are both conceptually and programmatically supported with use in survey weighted data. And how to go about testing this in Stata is unclear. There is no survey t-test in Stata and the disability combined status group was intentionally over sampled in addition to the education center design in sampling, so the survey element really is necessary in our analysis.

You can do a t-test with survey data in Stata using svy: mean as described here
Alternatively (as also mentioned at that link) you can use svy: regress and do weighted regression to get whatever mean comparisons you want. Similarly, svy: total will let you estimate and compare totals.