This might seem obvious, but new ranks would also require un-hardcoding rank requirements and bonuses... and here's an idea:
Most people would probably want for the new ranks to work as old Sergeant+ ranks (ie. just more officer ranks). How about allowing for an alternate option: a soldier can be given an officer rank, as normal (depending on the number of soldiers/officers), but he can also advance in non-officer rank (like, from squaddie to veteran squaddie, to elite squaddie), ex. based on the number kills*missions - this would allow to see the approx quality of a soldier at a first glance - frankly, I don't like "squaddies forever" syndrome which happens when there is no place for new officers anymore. Naturally, as soon as any officer's post opens, such veteran/elite squaddie can be promoted as normal. This would basically require breaking up the ranks into 2 categories: soldier ranks (based on experience) and officer ranks (based mostly on the total number of XCom soldiers).