Short Answer
The short answer is no, it's not possible to combine together two conventional fire alarm panels to make a bigger fire alarm panel. There are too many problems.
Long Answer
Fire alarm systems are building-wide systems. There can only be one control panel for the fire alarm system.
If the manufacturer does provide more than one control panel for a fire alarm system, what the manufacturer has actually done is to split the one control panel so even though there are two or more connected control panels, the two or more connected panels are actually working together as one; the two panels have to be networked together.
The system has to be made by one manufacturer. If the two panels are made by two different manufacturers, the two panels really make up two separate fire alarm systems. Two separate fire alarm systems trying to control one fire alarm-controlled area is a dangerous conflict and should not be attempted.
Listed for Use
Looking at it from a legal perspective, unless the two different panels are "Listed for Use" to be used with each other, trying to use them together is against NFPA Code, and many other codes. Each of the two different manufacturers will not cooperate with each other to get their panels "Listed for Use" as a combination.
Elevator Capture
If it's for an elevator upgrade, the elevator fire alarm panel has to be addressable, not conventional. A conventional fire alarm panel doesn't have the number of outputs necessary to properly "Capture" the elevator.
The addressable control modules have to be within three feet (one meter) of the elevator controls inside the elevator machine room, and there have to be an absolute minimum of three outputs.
It is possible to use an addressable "Slave" panel for the elevator, while still using the installed conventional panel as the "Master" panel. However, there has to be enough zone inputs on the conventional control panel. Also, the elevator inspector and the fire marshal have to both agree that using a master/slave combination is allowable to them.
Another problem is for the building's management to reset the Master/Slave panels; the management has to be trained to understand the reset procedure. And then, when the management personnel are changed, the new personnel have to be trained again, and again, and again. Sometimes, the new personnel never even hears about the extra fire alarm panel. In other words, continuous retraining is a nightmare.
Often, it's the firefighters that reset the fire alarm system after an alarm. They're trained to extinguish fires, not as fire alarm technicians. The reset procedure has to be the same for your building as it is for all other buildings. If the reset procedure is different for each building, trying to train the firefighters in the proper reset procedure for each and every building is impossible.
Save Money
Technically, trying to use a second conventional fire alarm control panel, even next to the first control panel probably won't work. If it works, just resetting the system is a nightmare, and the client will keep requesting new training sessions for the building management.
Legally, unless the two panels are "Listed for Use" with each other, combining two panels is an incredibly bad idea to try.
If you need to increase the number of input zones to the fire alarm system, upgrade the fire alarm control panel so it has more input zones.
If you need to increase the number of horns and strobes, install a Supplemental Notification Appliance Power Supply (SNAC Power Supply). An SNAC power supply, also known as a Signal Power Expander (SPX), Booster Power Supply, or some other name, allows more building Notification Appliance Circuits (NAC) to be used.
At this time, consider upgrading the conventional fire alarm system to an addressable system. Many of the addressable fire alarm systems are expandable. It's easier to make further expansions to an addressable fire alarm system than it is to expand a current conventional fire alarm system.
Douglas Krantz 
