I have a 5 year old Mason BB. The left side of the case is not parallel to the straight portion of the right side. The left side gradually juts out as one moves from the front to the back of the case. Although I'm not sure I'd guess this design is done to make the soundboard larger or to be able to position the bridges in some way.
I'm curious if this non parallel sides design is common in grand pianos and which other makers design their piano this way.
It is a common, but not universal, practice. It is probably a carryover from the early flatstrung designs that needed more room to the left of the bass bridge. It was certainly possible to angle the strings to the right (from the pianist’s perspective) but this crowded the bridge pin spacing on the bridge resulting in frequent bridge failure as string tensions steadily increased.
It is often claimed that this feature increases the soundboard area but this is not necessarily the case— soundboard area is a function of the relationship between the two sides of the rim—nor, beyond a certain point, is it particularly advantageous. In the M&H Model BB the tail is relatively wide while in the Steinway Model B it is relatively narrow yet both flare the bass side of the rim. Both pianos are capable of good, solid bass performance.
In theory the practice should be more advantageous—but is used less often—in very short grands. I suspect this is so because so many of what are called “modern” grands trace their design roots back to the early Steinway pianos. Many, if not most, of the smaller grands trace their design roots back to the many designs that came out of roughly the 1920 when the emphasis was on low cost and production technologies were changing rapidly. It wasn’t until NC and CNC machinery came along that building grand rims with flared sides became economical and very few, if any, short grands have been introduced since that time.