I'm a tall woman with 36DDD wants to go up a size. Any suggestions? (photos)

Based on these photographs you look like an excellent candidate for a breast augmentation.  It would fill your upper pole.  You most definitely could look natural if you chose the right surgeon and the right implant.  If you want to go larger, then it is the right choice for you, regardless of the size of your bra.

I would suggest meeting with aboard certified plastic surgeon. Let him/her examine you and tell you what would be best for the look you want. Triple D is a fairly large breast, and adding an implant may give you neck and shoulder discomfort.

Thank you for the question and picture.  Despite your good description of goals, online consultants will not be able to provide you with specific enough advice to be truly helpful. Ultimately, careful communication of your goals (in my practice I prefer the use of goal pictures, direct examination/communication in front of a full-length mirror, and computer imaging) will be critical. 
Generally speaking, the best online advice I can give to ladies who are considering  breast augmentation surgery ( regarding breast implant size/profile selection) is:
1. Concentrate on choosing your plastic surgeon carefully.  Concentrate on appropriate training, certification, and the ability of the plastic surgeon to achieve the results you are looking for. Ask to see lots of examples of his/her work.
2. Have a full discussion and communication regarding your desired goals  with your plastic surgeon. This communication will be critical in determining  breast implant size/type/profile will most likely help achieve your goals. 
In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. I have found that the use of words such as  “natural” or "DDD cup” or "up in size" etc means different things to different people and therefore prove unhelpful.
 Also, as you know, cup size varies depending on him who makes the bra; therefore, discussing desired cup  size may also be inaccurate.  Again, the use of computer imaging has been very helpful during the communication process, in our practice.
3.  Once you feel you have communicated your goals clearly,  allow your plastic surgeon to use his/her years of experience/judgment to choose the breast implant size/profile that will best meet your goals.  Again, in my practice, this decision is usually made during surgery,  after the use of temporary intraoperative sizers.
I hope this (and the attached link, dedicated to breast  augmentation surgery concerns) helps. Best wishes.