FUE in 2 Stages?

4000 grafts may make your donor area look very thin especially if you keep your hair short.  There is no way to work around the fact 4000 FUE as it is taking 4000 grafts from the donor area.

Most
people with healthy donor area can easily support 4000 grafts or more for their
transplant.  It does not really matter if
the two days are back to back or with a gap. 
Many people in our practice do it back to back just to get done and over
with.   That way the swelling, redness, hair washes and
other post op problems are all at once.  You
need to talk to your doctor to see what he recommends and whether or not your
donor area can support the numbers of grafts.

You do have a valid concern. First, I should mention that you should not do all 4,000 grafts in one day it should be definitely split. In my experienced, out of 1,400 cases that I've done, I generally I do not have a significance problem. In fact, I have perform 20 patients over 5,000 grafts each and I will publishing a paper that will show not a significant thinning in donor area. I use a product called Acell. This a growth factor from the inner lining of pig bladder. Although not magic it promotes better wound healing. I used  this in almost all of my FUE cases I have had very good results even though there is some thinning in the back of the scalp I have never had any patient who complained about it yet so far.

Two procedures of 2000 generally has better survival than 1 of 4000 and gives you the option to reevaluate your donor area after the first procedure. 4000 grafts is a long day, and graft survival is undoubtedly lower.

Many patients do their hair restoration in stages.  If budget is not a concern, I encourage them to do the high end of the recommendation as although its not a tough procedure you may likely have better options to spend a day.  In addition, your then pushing your total result out longer as it takes a year for the full result.

Donor management and the areas of where your grafts are harvested within the donor region is very important. You donor should be OK after 4,000 grafts and there shouldn't be a cosmetic difference or a thin look if you have a strong donor region. 

Accordingly to the density and quality of your donor area. You also want to verify with the clinics you got your quotes from if they are counting the number of grafts from the extraction phase or the implantation phase. If you are worried about loosing too much density following one procedure I would recommend doing 2 (with a minimum of 1 year apart) so that the skin has time to contract and regain it's density in between both procedures.

I would recommend doing it in 20 stages. Anything over 2000-2500 grafts is called a megasession and the success rate can go down as well for the transplanted grafts. By breaking it up in to 2 sessions you can do the frontal hairline to start and then in a year do a second session to add density throughout the rest of the scalp. This also allows time to be strategic with harvesting so that the donor area does not get over harvested and it also helps to see where the transplanted hairs will grow in and then plan the next session around what hairs are already there. Strategy and patience are the 2 most important parts of any hair restoration plan.