For me, playing 4 has to be canon. Because I think linearly (which in itself is probably a bad idea considering time is not linear, it's a ball of wibbly-wobbly timey-whimey stuff...), and when I take on a "new companion" or I play a solo adventure, I am familiar enough with my Doctor's timeline in order to pick out the times where he's either alone, or alone enough to result in me playing alone.
The biggest thing when playing a canon character is being familiar enough with your character's timeline to play it the way you want to play it. For instance, if I play the Doctor in Season 15, I know that he's either left Sarah Jane and hasn't met Leela yet, which would place the story between The Hand of Fear and the Face of Evil, where he was alone.
Also, another thing you can do is give your "fellow characters" an excuse to be alone. For instance, If I play a Season 18 Doctor, canonically he's either with Romana, Adric, or Adric/Nyssa/Tegan. So I give them something to do somewhere in the TARDIS that makes the Doctor be alone. It's almost like playing an NPC, but with less work.
Remember that playing canonically is completely up to you. But for those that do, remember that not all of the Doctor's adventures happened sequentially. The episodes that you see didn't happen one after another. There's so much that happens when we're not looking. It's more prominent in the new series than it is in the classic series. If your character is like Clara Oswald, the Doctor drops her off after every adventure, or so we see. So the Doctor has alone time, along with Clara. So they have plenty of time for fun and games!
If your character is like Donna or any of the classic series companions, the Doctor didn't drop them off. They hung out in the TARDIS in between adventures and such. So, it's harder for them to be alone, but it's more of an excuse to other TARDIS things to happen.