I had a Trådfri remote paired with my lights but wanted to add a second remote. Googling returned a lot of contradicting information. In the end the following steps lead to success:

1. Reset the new remote (just to be sure). Remove the cover at the back of the remote. Press the button inside 4x (within a 5 second span). On the front a red led should light up
2. Now grab the already paired remote. Remove the cover on the back as well. Move the remotes close to each other and keep them close for the next steps,
3. Press the button at the back of the new remote first and keep it depressed.
4. After 1-2 seconds press the button at the back of the already paired remote as well and keep it depressed.
5. At first the lights at the front of the remotes should be blinking rapidly but after 5-10 seconds they should both settle on a slow a steady pulse.

That’s it. Both remotes should now be able to control the same lights.

If it didn’t work just start again from the beginning. Just make sure not to reset the already paired remote or you’ll have to pair it with all the lights again!