Can you meta-analyze multiple outcomes of a single experiment? Suppose there is an experimental design where the test participant is randomly assigned to 1 of 3 conditions (1 control, 1 treatment, 1 placebo).
Each participant then completes 6 different measures of depression (so 6 dependent variables), e.g., 1) BDI, 2) CES-D, 3) EQ-5D, 4) HAM-D, 5) MADRS, & 6) SPSI-RTM.
The analysis includes pairwise comparison of all groups (3) for every depression measure. So, this gives us 3*6 = 18 total comparisons.
If I want to run a meta-analysis on the treatment vs. control, can I include the effect sizes of all 6 dependent variables and treat them as independent studies? Or would this induce bias due to them being from the same study? Is there a way to control for the correlation between DVs?
If I want to also look at treatment vs. placebo, can these be included in the same meta-analysis or do they need to be run separately?

You'd want to have the estimated differences (or by arm outcomes) and their covariance matrices to correctly reflect how everything is related. If you take a regression analysis approach, there's no particular problem - other than finding a software that will do this for you, for which e.g. the brms R package with it's fcor functionality is one option - with putting these all into a single regression model. Of course, you then still have a multiplicity question (i.e. at what level do you want to control what kind of error rate), which is less of a technical statistical question.
This is even clearer, when you want to compare all drugs in one class vs. placebo, and in one study you have two arms with different drugs from the class vs. placebo (3 arm study). In that setting, you cannot treat the two comparisons of the two drugs vs. placebo as two separate trials, because you wrongly double-count the placebo group. That's a pretty common mistake that keeps common up in meta-analyses.
