Yes you can hook the common of both transformers together. But you must phase the transformers. When you have them hooked up common to common, set each with an output voltage, and touch the other outputs together. If the produce a large spark, unplug one of them and reverse the plug in the socket and touch again. If they are phased they should not spark or barely spark compared to being un- phased.
You did not state the make of your switches, the type of transformer or its wattage. I do not know if you need 18 volts to operate the switches. If they are Lionel 1122 or such usually need 14v and have two lights on the controller and one light on the switch they will constantly draw 4 or 5 watts times 9. Additional wattage will be drawn momentarily when switching. These type of switches will add up and you are wise to get a separate switch transformer. I run Marx 1590 switches, 31 of them and they do not have lights and draw zero wattage unless switching. I use a small 40 transformer that outputs 14 volts with no issues.
Charlie
