Adding external antennae to factory radio

The short answer is yes, as long as your add on antenna comes with it's own cable.

I would check to see why the OEM antenna isn't working first, they use a wire embedded in the rear window grid. They do however use a long cable with multiple connectors that can corrode. That has been know to happen and they issued a TSB to replace the cable It used part number 4W1Z-19G323-AA to repair the problem, not sure if that would still be available now though.

You would not want to mount it in any hidden location or behind any panels as that would block the signal and would likely be even worse than the current unit. The short antennas also do not receive very well due to their size. If you want one that will work well you will want to mount it outside with a solid ground plane of metal under it for the best reception.
The connector will also be an issue as the common motorola connection isn't used on your car, it uses a Ford specific part, but there are adapters for that.

It won't cause an issue with the defrost grid. The repair kit that Ford offered can be attained online, it's just a defrost grid repair pen. Mounting an antenna behind the bumper won't be the best location for reception but it'll beat not having one at all! And you can get the adapter online for your radio.

The part in my post isn't a circuit repair pen it is a wiring harness update for the Lincoln that has an updated HAM that includes a signal booster and updated cable and power harness to match. The base part number for the booster only is 18K891.

That looks like an added on receiver for remote start and alarm.

You would need to find the place where the module is hidden, usually in the area under the steering column, then look up the model an see what it takes to make it work. What buttons does your remote have? Can you take a picture of it and post it. There are a lot of factory installed remote starts and keyless entry parts that were really dealer installed for extra money.

Okay, that is the factory system with the extended range transmitter. That should be the OEM receiver set up with the antenna box, most were dealer installed and there were a few versions. The remote start ones usually have a key on the blue button while the door lock only ones have a trunk symbol. There are also ones without the trunk control and remote start only. The remote start systems added on a module that sent a signal to the PATS system so the engine could start without the key.

Roger that SteveW! I got that TSB mixed up with one that we normally would use back in the day. I've never used that TSB or know anyone that has ever used that TSB but anything is possible!

I knew of it because the same basic part was used in a couple other Ford vehicles to cure radio issues. I never understood the companies putting the antenna in the glass. First car I worked on with that was the Vega. They worked on AM if you were less than 50 miles from the tower but on FM you might not make it out of sight of the tower. They are better with the selective antennas and a booster but I guess the companies figure nobody listens to radio anyway.

Not with that version. They are essentially the same thing, but the one with remote start uses another module, that your car doesn't have, to trigger the PATS system and makes it think there is a key in the ignition, then it uses the signal that activates the trunk in your version to trigger the starter in the remote start version. So you either have remote start or the trunk release. Sorry.