I know that level 65 is the top level for player characters; however, what is top level for companions? I have seen companions over level 65. In fact, I have two at 66.
It depends when you recruit the companions. If you are at max level ( 65 ) the companions you recruit after that will be a higher level, sometimes 2 to 3 levels above. This is to take the stress off training the new recruits.
You cannot train a crew member higher than your pirate, either with tomes or brawlin'. However, when you acquire a new companion, they generally are added to your crew at a higher level than your actual pirate -the amount varies (I imagine there is a formula, but I haven't studied it enough to say what it might be). So, when you see crew over level 65, it is because they were recruited by a pirate who was at level 65 or just below that level.
For example, with the new class companions added with the recent upgrades, my level 65 pirates recruited them and they came in as level 66 companions. When I bought a Hoodoo bundle card and assigned Hoodoo Cornelius to a level 65 pirate, Mr. C. came in as a level 68 crewman. As far as I know, level 68 is the current ceiling. I certainly don't have and have not seen any higher. But, they could be out there...
The only way to get Companions over level 65 is to recruit them when you are a lower level (ie 63 - 65) since, when you recruit a Companion, that Companion's level is usually 2 to 3 levels higher than your present level.