I can see two options here, use the existing system or add a new system.
Creating your own career paths
The most obvious option is to create new career paths (Rogue Trader, p39) which represent the multi-class Astropath Navigator or Explorator Void Master careers etc, but this could be quite a lot of work.
You would need to plan out the whole of their potential careers, and ensure they are balanced before your players chose their initial characters and then possibly have them say 'Nah, I'll just stick with a standard X'.
Possible multi-class system
A simpler solution might be to start a character with a single career, but allow them to take on a secondary career, with suitable role playing, once they have acquired all of starting skills, talents and gear of that secondary career.
For some pairs of careers the synergy between them will make this easy (shared starting traits, or secondary starting traits from advances available in the primary career) but for roles with less synergy it would be much more difficult, requiring you to take multiple Elite Advances (also Rogue Trader, p39).
Some Elite advances might require significant story events, such as the Astropath being sucked into the Warp and the ships Navigator reaching in rescue her only to have their minds merged in the resultant psychic contact (plenty of corruption and insanity points there) and her original body being left in the warp (and coming back later in the campaign inhabited by a demon). That sort of thing could make for some excellent role playing opportunities.
I would then suggest that while skill and talent advances could be taken from the primary career as normal, advances could only be taken from the secondary career one rank below (thus you would need to be rank 2 to take on a secondary career).
This could even be extended to allow tertiary careers (starting at rank 3, using rank-2 to determine advances from that career etc.).
The toughest thing is how to deal with Characteristic advances. The simple solution is just to use the advance scheme from the primary career and be done with it. For some combinations of classes this could seriously disadvantage the secondary career though.
What I would suggest in this situation is to allow the player to switch around advances from the primary career without altering that balance of that class, so the Astropath Navigator could switch the Astropath BS 500/Ag 250 to be the navigators BS 250/Ag 500, but couldn't get the Navigators Int/Per/Will 100, since the Astropath only gets 2 cheap characteristic advances in the first place.
Either way it is going to be work both for you as GM and for your players, but it could result in some very interesting stories.
One final warning is that if you have munchkin players, there are almost certainly some synergies in the system which might be unbalancing, and not easy to spot. If players get out of hand, there are plenty of techniques you can use to prevent them spoiling the game for others, but in Rogue Trader, the easiest is probably to pile on the corruption and insanity points as they get mad with their own power (Rogue Trader p296).