The maximum combined number of buttons on button modules per system is 1024.

1100 KEM: +18 (Max 3 per phone, 56 per system)
Add-on for 1120E and 1140E phones. Each module provides 18 additional programmable buttons.

1200 KEM: +12 (Max 7 per phone, 85 per system)
Add-on for 1220 and 1230 phones. Each module provides 12 additional programmable buttons.

BM12: +24 (Max 3 per phone, 42 per system)
Add-on for 9508, 9608, 9611 and 9641 phones. Provides 12 physical buttons assignable in 2 pages for 24 programmable buttons in total. When used with a 9508, power must be supplied to the phone using an inline power module.

BM32: +32 (Max 3 per phone, 32 per system)
Add-on for the 1616 phones that provides two columns of 16 buttons. Up to 3 BM32 modules are supported with any 1616. However, when used with more than one module the telephone must be powered from a power supply unit rather than PoE.

JEM24: +24 (Max see below)
Add-on for the J169, J179 and J189 phones. The modules automatically match the display settings of the phone to which they are connected (color with J179/J189 or greyscale with J169, font size, background image, screen saver).Note that the modules behave differently depending on whether attached to a J169/J179 or a J189:

J169/J179 Telephones (Max 3 per phone see below, 14/42 per system)
Both the J169 and J179 telephones can support up to 3 JEM24 button modules.

A single JEM24 supports 72 programmable button slots. These are arranged in 3-pages, with pages accessed using the module's page scroll button. When in 3-page mode, there is no indication of when programmed button slots not on the page being displayed are alerting. In this mode the module counts as 3 modules for the system's supported capacity.

When multiple modules are connected to a phone, each module only supports a single page of 24 programmable button slots and counts as a 1 module for the system's supported capacity.

J189 Telephones (Max 2 per phone see below, 14*/42 per system)
A J189 can support up to 2 JEM24 button modules.

Each module provides the phone with an additional 24 programmable button slots in a single page. That is, the first module shows buttons 49 to 72, the second buttons 73 to 96. The page scrolling buttons on the modules are disabled.

To support more than 2 button modules, the phone must use the J100 5V mains power supply unit rather than PoE.

DBM32: +32 (Max 3 per phone, 32 per system)
Add-on for the 1416 phones that provides two columns of 16 buttons. Up to 3 BM32 modules are supported with any 1416. When used with a DBM32 button module, the telephone must be powered from a power supply unit.

EU24: +24 (Max 1 per phone, 8 per system)
Add-on for the 2420, 4620, 4620SW, 4625, 5620, 5620SW and 5621. Provides an additional 24 programmable buttons. Button display icons are on two switchable pages with 12 icons on each page.  

EU24BL: +24 (Max 1 per phone, 8 per system)
As per the EU24 above but with a backlight function to match the 4621. Not supported on the 2420.

JBM24: +24 (Max 3 per phone, 42 per system)
Add-on for the J169 and J179 phones. Each module provides 24 dual-LED programmable buttons with information display adjacent to each button.

To support more than 2 button modules, the phone must use the J100 5V mains power supply unit rather than PoE.

JEM24 and JBM24 button modules cannot be combined on the same phone.

KLM: +48 (Max 2 per phone, 21 per system)
Used with M7324 phones. Up to 2 buttons modules are supported per phone. Each button module provides 48 programmable buttons.

SMB24: +24 (Max 3 per phone, 42 per system.)
Supported with 9608, 9608G, 9611G, 9641G and 9641GS.

T7316E KEM: +24 (Max 9 per phone, 42 per system.)
Used with T7316E phones. Each button module provides 24 programmable buttons. Up to 4 buttons modules are supported per phone without additional power supply. From 5 to 9 modules can be supported with additional power. Maximum 9 per phone (4 without additional power).