When I do my long endurance rides I need a third water bottle but only have two bottle cages on my bike. There isn't anywhere to purchase additional water on my long route. Any suggestions on how to carry this third bottle would be appreciated.

There are bottle cage mounts that attach to the saddle or seatpost and give you one or two bottle cages behind the saddle. More often used in triathlons but also an option for road bikes in your situation, rather than using a hydration pack you wear on your back.

Here's an example: Aquarack ii

Triathlete's double bottle holder behind your seat? handle bar mount, camel back bladder in a pannier, if not on your body.

Make your own water with a Sawyer or Platypus filter.

Jersey pocket, etc...

• Tri-bike behind-the-saddle holders.
• Fork mounts (A friend uses these on his long distance gravel grinder.)
• Handlebar holders, once popular in European road races (Google for pix from before the 1970s). Some triathlon and endurance riders still use these with drinking tubes.
• Frame bag, with narrower elongated bottles and drinking tubes.
• Collapsible reusable Mylar water pouches.
• Jersey pockets.

I may do the jersey pocket thing myself next long ride. I ran out of water Saturday. Weather was cool and overcast for August, since we're at the far outside reach of Hurricane Harvey. But I still underestimated my water intake because I was pushing harder on climbs. Fortunately family fishing at a nearby lake had a spare bottle of water. I was on the verge of dehydration and feel some of the effects today -- headachey, etc.

I always use a saddle bag for necessities so I don't really make much use of jersey pockets. Maybe a cell phone in the leftmost pocket, sunglasses and reading glasses in the right, spare bandanna and shop rag in the middle for wiping sweat. But next long ride I'll carry a spare disposable water bottle in a jersey pocket. The disposable bottles can be crushed and collapsed so they're easy to tote to the next available trash can. I also have a collapsible reusable Mylar water pouch. Prepped it for Saturday's ride, freezing it, but neglected to bring it along.

Quart bottles help a lot.
wiggle.co.nz | Elite MaxiCorsa 950ml Water Bottle | Water Bottles

Hi, as mentioned above, bottle cage that can be attached to the saddle or seatpost seems to be the most comfy way. Good luck,
Andreas

Camelback or similar.

Adding Water Bottle Cages to Bicycles without Braze

TimothyH gave you the canonical link for dang-near every option out there, but if you want to go straight to the source, this is what Minoura specializes in, at least for on-bike options. If you want to carry the water on your person, I'd go with a Camelbak.

You can get saddles with extra braze on mounts so you can attach darn near any standard bike accessory to the back of the seat. They come standard on Specialized fitness style bikes this year. Most LBS's (that sell specialized bikes) will have a pile of them for cheap they accumulated by selling a better seat with a new bike.

X-Lab also has many good options for behind the saddle water bottles. They also sell between the arms water bottles but that is more for Tri bikes than road bikes.