I have had some ideas for using a Photon with Carloop and other devices, but have not had the chance to do anything along these lines yet.
For SPI, the Photon has hardware support for SPI on the sets of pins in the Photon documents here:
That part was easy enough to find. The next part is the Carloop design, which is not quite so easy to find, but is on GitHub here:
In comparing the two, the pins for the 'SPI' Object are A2-A5 and are not used by Carloop. These pins are all available and you can use it to do SPI, so this should be quite easy.
Looking more closely, there is a design in work for a CarloopXL, which uses SPI for a SD Card. If that design eventually comes out, you would have to use multiple chip select lines (SPI-SS) for each device, such as A2 already used for the SD Card, plus some other available pin (D6 maybe to select your SPI display device).
One thing to keep in mind with your design is the performance. You will need to experiment to see how busy the Photon is taking care of the CANbus and the SPI to see if the performance is fast enough. It may be okay. If you are looking at performance issues, using CAN filters (see the Photon documentation) can help reduce the Photon workload in taking care of the CANbus.
Let us know how your project goes!