Fizz,
I have been a BA for over 15 years, and I face a similar situation. I need to show some career advancement. For me, much of this need is just about the money. However, doing the same thing over and over again gets repetitive. I too have become a generalist, skilled in many different software packages but not an expert in any one. Consequently, I have had many lateral moves and only a few promotions (which didn't change my responsibilities - just my title and salary).
Here are some possible career paths:
Business Analyst -> Sr. Business Analyst -> Lead Business Analyst (the obvious path, with some additional money and responsibility but not much more)
Product manager - In a software company, a BA can move into the role of product manager. Since this is a very non-technical role, it is a good fit.
Software architect - Many of the SA and BA skills overlap. This role focuses more on the functional software design than the "business" requirements. As an architect, though, you will be expected to understand a lot of technologies and platforms that Software Developers have a better grasp of. For example, you may need to know application servers, database servers, messaging platforms, etc. Software architect suffers from the same issue as business analyst. Where does this career lead?
Into the business - If you work closely with a certain functional group, you may move into a position doing whatever it is this group does. This leads to a "doing what the business needs" role instead of a "supporting the processes that do what the business needs". In other words, get out while you can.
Specialist of a technology or product - Find a technology or software platform and become the expert on it. If you use a certain supply chain software, become the expert on it. If you like business intelligence, learn a BI tool (all of which are geared towards very technical BAs - not programmers). Assuming these areas have teams to support larger processes or packages, you can become a lead or manager. This will not be a role where all you do is manage others. "Manager" means you keep doing, but you also have (more junior) people reporting to you. It means a lot more money. This can lead to further career advancement to the point where you no longer actually "do". The key to this is to select an area of expertise which allows you to build a staff. You can't pick a niche product/technology that leads to a team of one.
Specialist in a business function - Same general ideas as above but supporting a specific function. In your case, it could be supply chain. That domain expertise can lead to a role managing the software side of the business function regardless of the package or packages used. Your value is in understanding the domain problem and interfacing with subordinates (programmers and/or analysts) who know the software side of it. I have seen someone move from analyst to Sr. Director along this path.