We've been preparing for a long time. we have standard processes and think we're ready to go right to Maturity Level Three, skipping over Maturity Level Two. Is this allowed?
Sure, you can do anything you want. Oh, you also want to be successful? Why didn't you say that before?
Allowed? Yes. Practical? Maybe. Recommended? Not often.
When it comes to "Maturity Levels" the formal answer from the SEI is that you "should not skip levels." This has multiple contexts. First, you should not skip appraisal levels and second, you should not skip implementing the processes in ML Two. I'll address just the appraisal question here.
One reason it may not be practical is that, while some of the ML 3 processes areas are "built" upon the ML 2 PA's, some of the ML2 processes "stand-alone" and are foundational to the model (e.g.; Configuration Management, Measurement & Analysis). You'll have a lot of trouble being successful with ML3 without them.
I've worked with some clients that felt strongly that they were ready to jump directly to ML3 and I've advised them to AT LEAST conduct a less-formal appraisal (SCAMPI Class-B) on ML 2 prior to the formal appraisal to reduce their risk. Some have taken that advice and some have decided to conduct a ML2 Class-A just to be sure.
I don't usually recommend skipping appraisals because ML 2 is a very large effort and a huge accomplishment in it's own rite. In my humble opinion, the "jump" for ML 1 to ML2 is much larger than from ML2 to ML3 (it's a major culture change). Conducting ML2 first and then letting it "bake" for a while is a good thing for your organization and almost always results in a far higher degree of applied maturity in the end.