I met a female three weeks ago. You can read about our first date
here but I think it's pretty irrelevant to what I want to ask about now.
Basically when we met we both felt a connection, which was refreshing for me after months of using PUA techniques to woo girls who aren't that interested to begin with, and who I felt the same way about. Not putting PUA techniques down, otherwise I wouldn't even be here asking you guys! Of course I'm still using techniques on her, but now I'm looking for more relationship-oriented advice. But we are not in a "relationship." Let me explain...
Last night I met with her. It was our fourth date (not counting the night we met) and I felt like something was off. I asked her about it and she said that I was moving too fast and we needed to talk. But we were at a show and we agreed to talk later as opposed to yelling over the loud music. I did my best not to not change the way I've been acting with her and she reciprocated with touching, kissing, etc.
We went to a bar afterwards and I asked her why she thought I was moving too fast. Realize that we have been seeing each other no more than twice per week and basically everytime I've gotten in touch with her it was to set up a date (with a little bit of chat thrown in). Oh yeah and she has slept over twice. Sex has occurred. So I was really curious as to what I may have done that made her think I was moving too fast. She couldn't answer that, but told me that she is really happy being single, likes also some other guys (who I assume she is seeing) and doesn't want a relationship. But we agree that we have some kind of connection and she wants to keep seeing me. I haven't been friendzoned. She is still touching and kissing me.
I was totally cool about it all and told her I'm glad she told me because I want us to be completely comfortable and open with each other. She was happy to hear that and agreed (who the hell is gonna say "no, let's be uncomfortable and closed"?

) Since we were being open I told her that to be honest, I had been looking for a relationship, not to "own" her but just because in my experience men and women never allow themselves to truly open up and spend time doing fun things together unless they are "official." Basically I see lots of benefits to having a relationship but there is nothing I can do about it if she is not into it. I understand and want to keep seeing her. After this talk, which lasted for maybe 15 minutes we talked about lots of different things, I made her laugh, we made out, etc. And in the end I feel like we have moved up a level in this relationship which is not actually a "relationship!" She was very happy and glad that I understood. We didn't spend the night together because we both had to get up early. She gave me a goodnight kiss, had a big smile on her face, told me she had a lot of fun and asked if I was free to get together one of the coming days before she travels (in three days).
Today I sent her a message on Facebook about a couple trivial things we talked about yesterday (a song and a movie) and told her when I am free. I'm still waiting for her reply but not worried at all.
The reason I'm writing all of this is because I've never been in a situation like this before. I think it's actually a pretty good situation. I will force myself to keep sarging, have fun and learn more about pickup artistry. And at the same time I will have her, although I'm apparently sharing her with some other dudes. The thing is I feel like I have a very good chance of having her for myself -- the attraction level is very high and I think she might eventually give in and I will get the aforementioned benefits of a relationship. I will do my best not to count on it happening so I don't shift into needy/jealous mode. Whatever happens happens. But I want to know if you guys have any advice for me? Maybe some techniques I can use in this specific situation to try and influence her to come to the dark side

I suppose I need to keep building attraction and comfort, but do you guys have any specific tips that would fit well with this situation?