Badger
How long have you been studying the TSD, and why are you studying it? Now I'm not trying to put down TSD, but my question does help frame whether you should study two styles at once. I'm not against studying two different styles and I know (before any one points it out that BJJ and TSD are vastly different) but if your question about if you should mix two styles is an honest one (and I'm taking it that it is) then think hard about my question and it could save you some money and frustration in the process.
The question of how long have you been studying TSD as an adult helps to frame your experience level.
The question of why are you studying it helps to frame the answer to why study a grappling art and a striking art.
My current style, Tang soo do, is in my opinion brilliant. As someone who studied both karate and kung fu in my youth, I can see strengths of both in TSD. I have only one slight criticism. TSD is all about finishing a fight before it goes to the floor, so there are lots of strikes and throws and things, but not much for that dreaded but sooner or later inevitable situation, where you lose your footing and go down.
So I was thinking there is a Brazillion Ju Jutsu club in town, and I was thinking of giving it a go.
If you are planning on competing in a MMA type competition then it is a given to be a decent competitor you need to have some sort of background in ground work along with a stand up game. Enough said, go with the BJJ it is a proven effective system, and the TSD is also a good striking art and since you like it stay there.
But if you are not planning on the MMA type of events then, this is where the answer to your question gets murky and I go back to question #2 about why are you studying martial arts in the first place.
TSD is all about finishing a fight before it goes to the floor, so there are lots of strikes and throws and things, but not much for that dreaded but sooner or later inevitable situation, where you lose your footing and go down.
If you aren't trying to compete in an MMA type of sport, or you have no plans on meeting in the back alleys to try and test yourself against other street thugs, than why do you think you couldn't fight for real on the ground? I mean TSD has all types of strikes and kicks that even on the ground you can employ you just have to train for them. But this can be accomplished with kicking shields and focus mits and a training partner. I say this because training for them on the ground like this can further enhance your training in TSD and your understanding of that art as well as self defense. Plus you are staying in the art you like and are comfortable with while at the same time doing something that is out of your element thus forcing you to grow.
Now, more than 20 years on, some of the things that hold back my progress in TSD is that some moves are so similar to kung fu moves I learned years ago that 'muscle memory' makes me do the kung fu version rather than the version I am being taught.
Now I'm not sure which moves you mean here, but if you are talking about stances and things that can be a problem, but one you can get over. However you might also be over complicating or over thinking things as well. For instance in the systems that I teach, I recognize and embrace, that they are not "pure" arts that were passed onto me from the GM or the creator of the systems. I'm not studying or teaching historical heirlooms or something that cannot and should not be changed. So I started with the mindset to focus on more of the self defense(SD) side of the process and I adapt principles or techniques that I learned in Wado, Modern Arnis, or other arts but filter them through the TKD forms and system I learned and that I currently teach.
For the self defense part I freely take from my Modern Arnis and apply it to the TKD, even to interpreting moves in the forms, weapons defense etc. etc. For instance last night I was teaching my students an inside leg sweep using the knife hand block as the entry; however I learned the takedown at a JKDC seminar several years before as a silat move, the chambering of the hands for the fold and the execution of the block from Wado, the stance in the block is from the TKD I learned, the hand movement of the block and such is really more of the brush grab strike application that I learned in Modern Arnis with a little of Iain Abernethy instruction thrown in for good measure. My students learn this simply as an application of the knife hand blocks found within their forms and a foot sweep.
A silat stylist would tear apart the stance because I should have been in a forward stance, a TKD GM would maybe tear apart the chamber because I chamber like a Japanese stylist, the Japanese stylist would tear apart the back stance because of weight distribution etc. etc. but who cares it works. And I'm not passing down a pure heirloom style so I'm not bound to a long dead GMs thoughts or intentions. In fact the only person who probably would have liked this application would have been GM Remy because as he said "Modern Arnis is the Art Within you Art", and I was doing what he taught me to do.
So, I'm not sure what to do really. It seems there are pros and cons to mixing in another style.
There is pros and cons to mixing styles, but ultimately you have to have a firm base to mix from. I don't think you can start mixing without good leadership or guidance, or I should say it is more effective to mix stuff when you have someone to guide you with experience. I also believe this means more than just studying a ground game and a stand up game. People mix stuff all of the time nowadays,your TSD might also be mixed and not a pure system. In fact mixing styles and learning from other instructors is common in the Filipino martial arts, as well as in the Okinawan martial arts (where karate and TKD came from) so I think it is a natural thing to do.
However the big con to mixing styles nowadays I believe is thinking I must spend my money learning a totally different system to handle my self defense needs when that system is based on a sport or a heirloom and not SD in the first place. What I mean is this, one instructor told me about how he had a discussion with another instructor on how he (and I) weren't using the sai in it's original context when I translate double stick drills and disarms from arnis using it. In other words supposedly my swinging the sai in a backhanded motion wasn't the same as them swinging it in a backhanded motion since it wasn't (perhaps) in the same stance, hip twist, etc. etc. as in the kata. My position is who cares, I'm learning how to hit the person in both contexts. A back handed strike is the same either way and frankly hitting someone with a metal rod is still going to hurt. Often times people are to close minded to see.
I mean the sai was used as a (insert application here, I've heard it was a rice planter (poking holes in the ground) or some farm implement) anyway a farmer using it to defeat a swordsman is taking it out of it's original use context. I'm sure that poor farmer's thought when going against that swordsman wasn't on proper stance or his hip twist, but on hitting the guy and surviving.
How does this relate to learning a ground based martial art? This gets back to question #2 why are you learning and studying the MAs to begin with. If you feel you need to study BJJ to learn how to fight on the ground for anything related to SD needs then I think you time would be better spent working towards that goal then spending time and effort learning a ground game that is meant for a sport. Not that BJJ is not effective for SD needs, it is. It's just if your goal is to deal with getting knocked to the ground or to escape locks etc. etc. then kicking and fighting from the ground is good, so is ripping fingers back, pulling hair, sticking you fingers in the persons eye or fish hooking their mouth, etc. etc. all of which if you do to your seniors at the BJJ school is probably going to get your butt kicked big time.
I should point out that my motivation for training is not to win a fight. It is my intention, and always has been, to never fight for real if I can help it. Its just that its kind of my philosophy that if you're going to spend time, money and energy on anything, you should go all out and do the best you can do.
In closing if you aren't planning on ever having to fight unless you are attacked and it is for real, then you can still train for that, but chances are small that you will have to use it. So maximize your training to meet your goals and enjoy it. As an example at my sensei's dojo we spared like MMA; throws, take downs, leg kicks, body blows, you know all in good clean fighting (back in the 80's when there wasn't really organized MMA). I was young and I could take it. I learned to fight on the ground getting the fingers in the eyes and such, years later I went to seminars where we did this and had to deploy knives and fight from there. That was a small part of my training (time wise in the big scheme of things) and yet if I had to I can still do it. I didn't need to learn BJJ or a ground based martial art because that type of training (for SD) met my needs. Leaving me time to pursue other arts and further my training in my main art. I agree whole heartedly with your last statement which is why I still come back to question #2.