Can Airport Express bridge off another Airport Express?

My question is, If I place a third additional Airport Express outside on my deck/patio will this daisy chain off the current AirPort Express that is already bridged to the Airport Extreme Base

Sorry, but no. Although the third AirPort will connect to the AirPort Express, it will "join"....not extend...the network. When an AirPort "joins" a network, it provides no additional wireless signal coverage.

or will it ONLY be able to bridge from the AirPort Extreme Base

Correct, if you want the additional AirPort Express to "extend" the network. An "extending" device must connect directly to the main base station.....not to another device that is already extending the wireless signal. The reason for this is that Apple's "extend" feature only allows a signal to be extended wirelessly one time....not two.

if I do not receive signal from the AirPort Extreme base on my deck/patio will this be of no use to extend the range?

Correct. But, if you located the additional Express somewhat closer to the AirPort Extreme, it might pick up enough of the signal to be able to extend it. Remember, an extending device can only extend the quality of signal that it receives.

However, if you could run an Ethernet cable from the port on the current "extending" Express to the other Express that you want to add, you could configure the additional Express to 'create a wireless network" and effectively extend the network that way.

So in theory, I can run a cat5 from the 2nd Express to the 3rd express (out on the deck) and set it up as a secondary base network

No theory involved here, there is no problem with doing this. AirPort Setup in AirPort Utility 6.x will literally automatically configure the 3rd Express for you using the same SSID and password as the main network....so everything will behave as one "big" wireless network.

and if I wanted to have a 4th express (in garage), I can then "extend" it from the secondary base network created off the 3rd express?

I assume that you are thinking about extending wirelessly here, correct? You can do this if the 4th Express is located where it can receive a strong wireless signal from the 3rd.

I don't know if you have thought about this or not.....but there is one "weak link" in doing everything here, and that is that the operation of the 3rd and 4th AirPort will depend entirely on the quality of the wireless connection between the AirPort Extreme and AirPort Express 1.

Any problem between the AirPort Extreme and AirPort Express 1......and AirPort Express 3 and 4 will go down as well.

Bob. You are pretty knowledgeable on the airports. I just bought a time capsule and express last night. My router has to be in the kitchen so in the past I used an express as the base station and then an extreme by my printers and drives downstairs. This worked fine until my express stopped working (it was from at least 2009).

I am trying to "extend the network" from the express with a time capsule. It keeps telling though that it cannot find any base stations.

Did apple change things so that only extremes can be extended?