Does the LEGO Dimensions gateway portal work across multiple systems?

According to a Game Skinny article from 2015, only the Xbox portals are console-specific:

If you are playing using the Xbox 360 or the Xbox One, these pads only work with their respective consoles because of Microsoft's peripheral certifications. However the Wii U, PS3, and PS4 pads are interchangeable and you can use one with any of the three consoles.

In other words, there are three base stations:

• Xbox 360
• Xbox One
• Wii U ⟷ PS3 ⟷ PS4

Julio’s answer supports this by mentioning that Disney Infinity bases have the same restrictions on Xbox.

the WII/PS3/PS4-Version also works with Linux as USB-HID but needs there custom (python) scripts as RFID-Reader and three multicolor LED-Output-Device

To clarify the previous post, note that the Game Skinny article says,

If you are playing using the Xbox 360 or the Xbox One, these pads only work with their respective consoles because of Microsoft's peripheral certifications...

So the answer should be:

• Xbox 360
• Xbox ONE
• Wii U ⟷ PS3 ⟷ PS4

I also happen to have Disney Infinity bases for Wii U, Xbox 360, and Xbox ONE, and can tell you that each respective Xbox Infinity base ONLY works with its own console, but my Wii U base works on PS4 and PS3 as well. I would imagine that Lego Dimensions and SkyLanders bases work the same way, with 3 unique versions of the base manufactured to span across all consoles.

So, I know this is extremely late (4 years later) but at the bottom of your Lego dimensions base, there is a print in the middle. On that print it states the model number and the listed consoles it works for. For instance, mine says model/modelo No. ###### for ps3/ps4/WiiU