For information on stock/OEM controllers, see the /components/controllers.md page under Components.
There are a handful of aftermarket controllers that allow a more extensive range of modification possibilities.
There are a range of controllers for various HHKB models, including the Professional, Professional 2 (ANSI and JIS) as well as Bluetooth controllers for the Professional 2 ANSI and JIS models.
These controllers do not work with the HHKB Professional Classic or Hybrid series.
The Professional 2-compatible versions of this controller do not include USB ports (as on the factory controller). In place of USB ports, there are two LED indicators and a power switch that fit into the USB port cutouts on the Professional 2 case.
Reddit user /u/yangdigi created a series of controllers with Bluetooth support called the BLE.
A version for the Professional 2 line was released by KBDFans. /u/yangdigi also appears to have created a version of the controller for the Professional 1 line. This controller is no longer available for sale, and unfortunately KBDFans has taken the product page down, so there's not much more information I can provide.
This controller includes a few interesting features, including LED indicators that shine through the HHKB top case (potentially ineffective on charcoal cases), external USB ports (not present on the Hasu controller) and an additional internal USB port which can be used for USB drives or other small USB devices.
According to users, this module provided better battery life than the Hasu controller as of 2020.
This controller doesn't appear to support TMK or QMK firmware. The official firmware appears to be a fork of TMK.