Can I just upgrade to 5200 pound axles ?

Yes IMO. I had a similar situation. My last TT had 4400lb axles and 15" D rated tires. My current 5er has 5200lb tires and came with the same exact brand and size D rated 15" tire. The TT had a GVW of 8800 and the 5er is 11,400. Same size I beam on both.

Since the jump is not huge...I figured what is worse... over rated tires for the axle or an overrated axle for the tires... this is where this gets dicey. The older axles I have are 4400lbs. rated. If I could...could I just add another axle and spread the weight out under the frame? The dilemma is that there are no 4400 axles out there. Do not get me wrong ..I have the means to just add one on...or just stay with two axles that are higher rated and stick with just a tandem? Going with two new axles is more cost than trying to just add one and another set of tires...any thoughts?...I could just search for a matching axle or would adding one that was less or more rated be the wrong thing to do?

This would change where the weak link is in the rating, so ask do you really need all the extra capacity?
Tire ratings are engineering numbers and failures can be real messy and don't forget you need full pressure in them to have that rating and sometimes tires leak a bit before you notice.....

You can always upgrade axles to whatever you wish to install/fit on your trailer, Is it safe, maybe, does it increase your GVWR, probably not unless you have or know an engineer to determine the frame/hitch capacity of your trailer.
Without that, the only thing you can safely accomplish is to have an increased comfort zone knowing your tires and axles are plenty heavy enough and rated enough to haul your #8800. The same physical size frame from one trailer to another doesn't mean they are rated the same. Thickness of the tube wall or web, flange thickness and width of an I-beam flange also come into play to determine load rating. Just my opinion from working in the metal industry for 40 yrs.

Have to agree 100% with what tinner12002 stated. ;)

While the weight increase you are looking for is not huge, the RV industry is well noted for designing and constructing their trailers to just barely meet the GVWR going out the door. So that while you may be upgrading the axles, there well may be other very weak links which will be over their capacity when you go over the original GVWR.

Must agree with tinner12002 and 3oaks. The weak link is now the frame itself as it was probably designed for the 8800lb load and not much more.

Could I safely upgrade to the 5200 axles to give me a 10400 max load rating vs. the 8800 I have?

No....nor would 6k axle make your 8800 gvwr trailer into a 12000lb gvwr trailer.
10k gvwr RV trailers has the trailers shell (sidewalls/roof) strengths figured into its gvwr formula.
Trailers like a 10k gvwr car hauler/flatdeck and equipment trailers have a stand alone frame.

Take a look at a 10k gvwr stripped down rv trailer frame that some one thought would make a 10k gvwr car hauler.
The main frame rails on the 10k flatdeck trailer are much heavier plus it has close spaced crossmembers vs the rv trailer lightweight frame that would do well to support a 3000-4000 lb load.

Going to 5200 lb axle will give you a 6 lug axle for 16" wheels and LT E tires for 40k-60k miles and 7-10 years of trouble free service with the right tire maintenance. Check with Rockwell American axles or Dexter axles if going up to their 5200 lb axles would be a brake upgrade.

One of the reasons I picked my TT was the huge load rating. I have the 5200# axles often used on much bigger trailers.
I've also seen all kinds of TT's and fivers get thier axles upgraded and have never seen a problem.
These trailers just aren't that sophisticated that the frames are so highly engineered to include a bunch of formula's for body strength that they cant be easily upgraded.
And I'm sorry JimNLIN but the walls of my cheaply made trailer aren't stressed members - they're just built as cheaply as they can be out of styrofoam, luan paneling and vinyl wall paper. :D
The axles are nice though, it's great having nearly two tons of CCC!

Tires failures are pretty common. Bearings fail occasionally, too. How often do axles themselves fail?

Maybe quality tires and frequent bearing repacks might be money better spent?

...........Last I checked , 5,200 axles are NOT being mfged anymore ! So , you can move UP to a 8 stud 6k or 7k axle . Both come equipped with 2" wide x 12" electric brakes . You can purchase either 6 hole OR 8 hole wheels for existing 5,200 axles . , jf