This advice may not be popular here, but I recommend against multiple grade skips apart from exceptions below. When kids are little, skips tend to be fine because little kids don't really notice. But when the class gets to 8th grade or so, a double-skipped student is a little kid with peers who are adolescents. This really is a big deal, regardless of how it's downplayed among the gifted advocacy groups. I've met too many people who were multiple grade skipped and talked about high school misery to believe that multiple skips are a good idea for many/most kids.
Fortunately, there has been much research on this topic and the general consensus disagrees with your suggestion (I'm reminded that the plural of anecdote is not data).
Senior year in HS I was 16 when my girlfriend turned 19. Most others were 18. I had no issues and am quite glad I accelerated.
At the same time, I'm keeping my DYS DD in her grade for various reason. The IAS has some very good research-based diagnostics to help evaluate any specific situation. we were fortunate to be able to work with one of the authors.
Bottom line is that there's no "right answer", only one for each individual. But there is aggregated data from wide-ranging research.
