When it comes time to replace one or more of the tires on their RV many shop based on price, so they are
Do I need to replace all the tires at the same time or can I just buy one to replace the damaged tire or just a pair for the front axle?
Do I have to keep the same brand or size or design tire or can I make a change?
Lets separate RVs into two categories. Motorized units such as Class-A, B or C and Towables.
Towables normally have one, two or three axles and I believe that baring some mechanical problem such as bent or out-of-alignment axle or having had a puncture you will probably be able to replace two at a time so you can spread out the cost for new tires over a couple of seasons. You should replace both tires on an axle with identical size, brand and design as if you mix tires you will probably end up with the tires fighting each other which can cause irregular wear in extreme cases.
With four or six tires to worry about there is an increased probability for one to suffer a puncture before the rest of the tires wear out or "age out", so there are advantages to keeping all your tires, including the spare identical. That way if you need to replace just one tire you can use your spare and still end up with the same size, brand and design tire on each axle. If you do change brand, size or design on your trailer and then suffer a failure you may want to purchase two tires to keep all tires on that axle identical. If you take this route I would suggest keeping the spare that matches most of the tires on the ground.
A good bit of news for owners of towables. Since you don't have tires mounted in a "dual" position (dual means two tires on the same end on an axle) you do not have to worry about OD matching. With the shorter life of tires on towables it will definitely help with your budget if you plan and do rolling change of say one axle per year rather than all 4 or 6 tires at one time. I would also put the tires with the deepest tread depth toward the rear as rears are more prone to puncture and heavier tread will lower the potential for puncture.
Motorized RVs have a bit more to worry about. It is very important that all tires on each axle are the same brand, size, and type as mixing tires can cause steering, handling and even braking un-balance which could present
Previously I have discussed the advantages of confirming availability of tires that are identical to what you are using or you should strongly consider carrying a spare if you have a unique size or brand.
It is also critical that when replacing one tire of a pair of duals that both are within 3/4" circumference. If more different in actual measured size one tire will be forced to carry a greater portion of the load from that end of the axle and by now you should know that increased load can contribute to hotter running and in extreme cases.
Bottom Line Yes you can change tire Brand or Size or Type but I strongly suggest you do your research in the comfort of your home or at a campground rather than on the side of the Interstate and on the phone with the tire service company. BUT if you change tires you need to be aware of the potential for different and possibly unbalanced handling on motorized RV if you make a change, and the smaller (lighter) the RV the more pronounced this performance difference can be.
Having a TPMS is a good investment as it can warn you if you get a puncture and you may be able to stop soon enough that you do not damage the tire beyond repair-ability.