On which board can 32 bit Marlin run?
The  platformio.ini file, given in Zac's comment, does not seem to list all of the boards supported.

However, The Marlin 2.0 32-bit thread appears to have a table that is much more complete (at the time of writing):

Board                           MCU         State            To-Do
RAMPS, etc.                  Arduino AVR    good  
Due, RAMPS FD (v2.A!), etc.  SAM3X8E        good  
Archim 1.0                   SAM3X8E        ❓unknown    Only US$170!
Archim 2.0                   SAM3X8E        beta       needs confirmation
Re-ARM                       LPC1768        beta       NEOPIXEL_LED,M100,ENDSTOP_INTERRUPTS,Tones,etc.
MKS-SBASE                    LPC1768        beta       NEOPIXEL_LED,M100,Tones, etc.
Smoothieboard                LPC1769        beta       NEOPIXEL_LED,M100,Tones, etc.
Azteeg X5 GT                 LPC1769        beta       NEOPIXEL_LED,M100,Tones, etc.
Cohesion3D Remix             LPC1769        beta       NEOPIXEL_LED,M100,Tones, etc.
Selena Compact               LPC1768        beta       NEOPIXEL_LED,M100,Tones, etc.
Malyan M200                 STM32F103C8     beta       EMERGENCY_PARSER,NEOPIXEL_LED, etc.
Borg                        STM32F765ZGT6   ⚠️beta       EMERGENCY_PARSER,NEOPIXEL_LED, etc.
Chitu3D V3.9                STM32F103ZET6   alpha      EMERGENCY_PARSER,NEOPIXEL_LED, LCD, SDCard, MAX6675, etc.
Teensy 3.5                  MK64FX          alpha      (need shields)
Teensy 3.6                  MK66FX          alpha      (need shields)
STEVAL-3DP001V1             STM32F401VE     alpha      (need boards)


From [Question] Most promising 32 Bit Platform for Marlin 2.x


  The reference platform IS Re-Arm with a RAMPS shield. You can find instructions for both obtaining it and getting setup with it at #7076


It appears the you have to use the bugfix branch:


  Right now, there are two branches. Bugfix-v1.1.x and Bugfix-v2.0.0. They are almost identical from a feature set perspective. But Bugfix-v2.0.0 is modified to have a hierarchical file layout. That was needed to clean up the code and to support 32-bit.
  
  The AVR code is fully debugged and working in both branches. The 32-bit code only exists (and works) in the Bugfix-v2.0.0 branch. And while the code does work... And some people are using it to print, it isn't entirely painless to get to that point.


You may also want to read Recommendations for a good 32 bit microprocessor to run Marlin. To list a few examples:


Atmel ATSAM3x8e on the Due board
Anyhow, there are a lot of 32bit Controller. Take a look at mbed.org for example.
You can use the arm-none-eabi-xxx for STM32, LPC, also the Arduino Due use it
Duet board (now called DuetWifi) is available for pre-order. It has a 120MHz Cortex M4 with hardware FPU
AZSMZ ARM 32bit controller board
RedBear: https://redbearlab.github.io/arduino/package_redbear_index.json


RedBear Duo (Cortex-M3, WiFi + BLE)
RedBear discussion forum

Konekt Dash/DashPro (Official): http://downloads.konekt.io/arduino/package_konekt_index.json


Cortex M4-based global cellular dev kits, support for all board variants, support for USB and over-the-air programming straight from within Arduino IDE



Another link that might be useful is Unofficial list of 3rd party boards support urls, although not all of these are 32 bit.