Have you considered an MBA? That's one way to increase your earning potential.

I think it all depends on your interests. For technical knowledge areas, there are usually part time short courses or seminars , delivered online or evenings for professionals, organised by professional institutes, local colleges, 3rd party training providers. These generally cost a lot so the best case scenario would be to get your employer to sponsor you. Then there are of course master degrees or postgraduate certificates delivered also part time or on a day release mode which can agreed with the employer. There is finally, an abundance of self paced courses or publications that you can review in your own time by yourself. All of course depends on what your interests are and generally requires proactiveness, motivation and medium / long term planning to fit around the work schedule of an architect. I personally have a lot of short courses planned ahead for the next year and I regularly search online for relevant courses I want to take. Hope that helps. 

If you're thinking you are going to earn a credential that is going to immediately (or even in the short term) lead to a higher salary, more responsibility, or even just consideration for non-entry level positions I think you're going to be disappointed. There really isn't a short cut to advancing in this field because so much is learned on the job.  Typically you just need to position yourself to be given an opportunity and then deliver when you get your chance.  If your firm isn't giving you opportunities then find one that will.  Show why you deserve responsibility before you ask.

That being said, you could go the software route and really learn Revit/earn a certificate and pursue a BIM Coordinator type position.  In my opinion it would be difficult to really be effective as a BIM Coordinator/Manager without quite a bit of experience through all project phases and a variety of project types but I've never been in this position so maybe I'm mistaken. Still just my opinion, but while I don't see BIM Coordinator/Manager as a dead end, I also don't see it really opening a lot of doors.  It's not difficult to get stuck in a position like this because other members of the firm will become so reliant on them.  Lot's of cleaning up other people's mess.

Parametric design, python, etc. might get you into a position that isn't your typical entry level designer but I'm not sure it's going to lead to the range of experiences you're going to need if you want to run your own firm.  This seems like a high probability of getting pigeon holed as a software person (this applies to all design software as well) but I honestly haven't worked in a firm that does parametric design or is using python or anything similar.  Perhaps try to speak to some individuals in these positions to understand their experiences.  In the midsize firms that I've worked in the people that are really good at sketchup, photoshop, etc. end up spending almost all of their time modeling and very little putting together a set of drawings or learning to coordinate with consultants, clients, or contractors.

Another route is project management.  I believe academic courses as well as the more professional type offerings robhaw mentioned could fit here.  If your firm uses a specific project management software it would be good to know.  Understanding scheduling or gaining a basic understanding CM software like Procore might be helpful.  Project Management will open doors and will benefit you if you truly pursue your own firm.  However, regardless of your ability to use the software a firm isn't going to let you manage a project straight out of a MSc.  Even with some kind of degree you are going to have a hard time convincing a firm to hire you and let you manage a project without experience.  At that point you probably aren't doing architecture or getting AXP hours.  I think this option makes more sense as professional courses/seminars after a few years of experience and understanding how your specific firm operates.

All of that was a long way of saying just focus on getting your AXP hours and then pass the ARE's.  Instead of postponing your professional career with another degree or stretching yourself trying to work, achieve licensure, and gain some additional skill you may or may not use, just focus.  Enjoy your social life and don't burn yourself out.  Plenty of firms offer raises and promotions for licensure.  It will definitely make you more marketable when job hunting in the future and likely lead to higher salaries for your experience level.  You might even be able to get some side work that will allow you to brush up on other skills.

In my opinion, you can take every class that exists but you won't be as employable as someone with work experience.  It takes longer than 2 years of experience to learn how to run a firm. Through working, you figure out what you don't know, what your strengths and weaknesses are, and what you enjoy doing. Get out there and see what you enjoy and what you are good at and evaluate from there what classes or courses may be of additional use. A big part of owning a firm is managing people; you learn that by being managed and seeing how others manage. A great manager isn't just profitable on paper.