Can I delete excessive number of multivariate outliers, like over 10% in sample? I have a dataset with around 9000 cases, I'm running a factor analysis and I have found that 1100 cases are identified as being a multivariate outlier.  Is it alright for me to got ahead and delete it?
 A: In addition to @karl broman's excellent point, I'm curious as to how many variables there are.  You  could be running into the "curse of dimensionality". 
Also, I would NOT delete outliers just because of some arbitrary threshold.  You haven't said what it is you are studying, but, often, the outliers are where the interest is.
And I strongly agree with @Karl 's point about looking at graphs first - LOTS of graphs. 
A: While the above topics are interesting, with 171 items I think validity is going to be a concern that overrides statistical ones.  There's a real risk that people are going to answer mechanically, resulting in straightlining or in a very large initial factor that represents a halo or horn effect.  I think your team should be able to use non-statistical criteria to trim down the survey to a more manageable level that will make it more worthy of the statistical analyses you want to do.
A: It's hard to see how 10% of the data could be called outlying.
There's nothing that says you can't omit them, as long as you say clearly exactly what you did.  But, this particular instance seems a bit extreme.
When it comes to outliers, I first ask, are they errors?  If they're errors, I'd want to fix them; if I couldn't fix them, I'd be reasonably comfortable omitting them (though I'd worry about bias).
If they seem not to be errors (or there's no way to tell), I'd ask: do they affect the results?  If omitting them gives the same answer as not, I'd be happy and move on.  If it does matter, I would look for more a robust method of analysis.
I would look more closely at your method for identifying outliers: is it making some sort of assumption that is clearly wrong?
Most importantly, I'd look at lots and lots of different plots of the data, to see what it is that is leading those 10% of points to be called outliers, and whether it seems at all reasonable (though I can't see how it could be).
