How soon after you get a BBL with 360 Lipo can you add extra compression? If so, what is recommended?

I would ask your plastic surgeon about garments and the duration of wear, because each plastic surgeon will have a different protocol.   The patients who tend to have healing issues with larger volume liposuction procedures tend to be the ones who do not wear the compression garments at all, wear them very inconsistently, or do not wear them snugly covering all areas of liposuction. 
Our office provides our TT/lipo patients with an ADJUSTABLE compression garment manufactured by Clear Point.  The  patients like the support it provides to the back and to the abdomen.  The only complaint I have heard is related to the "itchiness" of the fabric which can be remedied by wearing a soft t-shirt under the garment.

Dear lledet09,
every plastic surgeon has his own postoperative protocol which he recommends to his patients. I would suggest you to discuss this with your plastic surgeon.
Daniel Barrett, MD
Certified, American Board of Plastic Surgery
Member, American Society of Plastic Surgery
Member, American Society of Aesthetic Plastic Surgery

Hello dear!!
Thanks for the question and provided information as well.
Every doctor has their preferences in regards to compression garments. I suggest my patients use a full body compression garment (that closes with clips), 24/7 for the first 3 months, and after that, for 12 hours a day for 3 more months, to get the best results.
It is important for the compression garment to be very tight, for it to help with the swelling, after surgery, and to use it with a cotton t-shirt underneath to avoid garment burns.
Please, follow up close with your plastic surgeon.
Good luck :)

It is best to ask your PS when you can wear a waist trainer etc. They can create permanent irregularities or indentations if worn to soon after surgery. 

You just have to be careful in the early acute postoperative period with compression garments that have rigidity similar to the concept behind avoiding jeans and stiff clothing as they can create permanent contour deformities. I would wait at least six weeks