One of the things that's been bugging me since I got the DH2 rulebook, is the immense difficulty in making a "balanced" character. Now I'm not necessarily meaning in the: "Character is OP" or "Character is underpowered" kind of balanced.

In DH1, through the career system, with the exception of the Cleric and Adepta Sororita careers, every career was "Balanced" at least terms of characteristic advances.

Each career had three characteristics they could take a 100XP advance in. three they could take a 250 XP advance in, and three they had to take a 500XP advance in.

In DH2 I find it's quite difficult to build a character that ISN'T either absurdly specialized, or the very definition of a Jack-Of-All-Trades, master of none. It seems like if I even push for three "100 XP" characteristic advances that almost certainly means taking 500 XP advances in literally everything else.

It feels like this would be a much easier if characters had an extra aptitude, to tilt the scales a little more evenly.

Or would that just encourage an overly broken character?

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TL;DR-- It feels like DH1 is to DH2 what D&D 3.5 is to Pathfinder. DH2 allows far greater options for character creation and advancement, but seems to encourage optimization and over-specialization towards "what you're good at".

Would adding an extra aptitude fix this? Or would that just lead to potentially broken parties?

An overly broken character happens if you have a player that seeks to make one. You can not trust the system to prevent this.

It is true that the aptitudes are not very well balanced, so if you want to address that you could be liberal with letting the players exchange aptitudes if their homeworld/background/role aptitudes gives them a poor selection. I think that is better than just adding an eight aptitude as it promotes a wider selection of character builds.

Alternatively you could go all the way and declare that everyone has all aptitudes and tune the xp rewards accordingly.

Search for aptitude(s), there are a ton of discussions on this topic. :-)

What I suggest is just making means to acquire more Aptitudes available; make some new Elite Advances that make sense (Stormtrooper, Mechanicus Magos, Judge, Preacher, etc.). You'll notice most Elite Advances do provide Aptitudes, and it is pretty nice way of providing more options and flavors for the characters.

I'm not sure that an extra aptitude will meaningfully fix the problem that the system as currently written will significantly encourage specialization. (This was an issue with the old pre-BC style of using charts as well, but in that case you didn't even get a choice in how to specialize your character.) An extra aptitude is certainly useful, but its effects are relatively minor compared to the first seven.* Thus it might paper over things a bit, but the major issue is actually the cost structure for purchasing advances. You may have noticed that it gives heavy discounts for having two appropriate aptitudes or heavy markups for having none, and hence fixing the problem of encouraging over-specialization would have to alter that paradigm. So here's a variant cost structure that I eventually worked up for my group. (I should note that neither giving an extra aptitude at the start nor allowing a one-time swap of several aptitudes fixed the problem of over-specialization in my group.)

Characteristic Advances: +5    +10    +15    +20    +25
Two Aptitudes           150    325    550    775   1000
One Aptitude            200    425    700    975   1250
Zero Aptitudes          250    525    850   1175   1500

Skill Advances:          +0    +10    +20    +30
Two Aptitudes           125    250    375    500
One Aptitude            175    350    525    700
Zero Aptitudes          225    450    625    900

Talent Advances:         T1     T2     T3
Two Aptitudes           250    350    450
One Aptitude            300    450    600
Zero Aptitudes          350    550    750

The rule of thumb here is that two-aptitude advances are more expensive (but still cheapest), while one-aptitude and zero-aptitude advances are never more expensive but usually less expensive. In particular, zero-aptitude advances are all notably cheaper under this scheme (but still most expensive) so as to not discourage players from buying them. The old system's costs for such were basically so out of whack that players would almost never buy such expensive abilities, so one of my premises was that costs for zero-aptitude advances were effectively nonsense.

Hence I figured that I'd center things around a harmonic mean instead. Unlike the arithmetic mean, or the average of a set of numbers, the harmonic mean of a set is biased towards the smaller values in that set. And of course the smaller values in a set of purchasables are the ones most likely to be used anyway. In this case, my heuristic for varying costs based on aptitudes was at +/-50 * [difference in aptitudes] * [tier]; I figured that it was appropriate for establishing differences between varying aptitudes without being overly punitive.

As for other solutions, I'll note that my group merges the Psyker and Leadership aptitudes together (because each of the two, on its own, is really marginal) but also disallows gaining extra aptitudes from elite advances. As noted you've probably seen some elite advances granting an extra aptitude, but this doesn't actually fix the real problem. (Particularly because they tend to give out the marginal aptitudes that exemplify issues with the aptitude system as a whole!) My recommendation is to stick with some fixed number of aptitudes - seven or eight is fine either way - and to use the chart above.

*More precisely, it doesn't break the game if everybody's getting that extra aptitude. Intra-party balance or lack of balance is what really matters, because if the party is stronger overall then the GM can step up challenges to meet them as a whole. But if individual party members have a significant power disparity, then it becomes that much harder to the GM to judge appropriate challenges against the group.

Alternatively you could go all the way and declare that everyone has all aptitudes and tune the xp rewards accordingly.

This is what I'd suggest. Aptitudes look like a solution in search of a problem. I've seen people claim that they prevent players all building the same character. Which is a problem I have never seen when I play a lot of classless RPGs.

I've seen people claim that they discourage minmaxing. Yet I keep seeing people discuss choosing their homeworld and background based on the aptitudes it provides, not based on backstory/lore reasons. Which just smells of minmaxing, so it looks like aptitudes encourage minmaxing because they make character creation more complex and increase the power gap between the minmaxers and the players who choose based on backstory/lore.

Maybe also adjust the XP costs of advances. But keep them the same for every PC.

Aptitudes were a refinement of Black Crusade's system of having different costs based on what gods you were aligned with, and in general were intended to move the game forward from the previous system of grabbing advances off specific charts at specific prices. If an advance wasn't on one of your charts, then likely as not you wouldn't be able to purchase it at all. There was an option to Ask Your GM, but that wasn't a certain thing, and the guidelines for such generally involved paying at least double the usual cost. Hence aptitudes were intended to let players define their own class, in a sense, for their PCs rather than be straitjacketed by detailed and lengthy charts. And I'd argue that they're better than the old system, but of course how much better depends on the implementation of things.

You are correct that the current implementation does encourage folks to look at the pieces of character building (homeworld/background/role) for their mechanical value first. But that's a facet of the implementation itself, not necessarily the aptitude system as a whole. One way to deal with this, as I've argued above, would be either to rejigger the cost structure so as to not so heavily encourage specialization. But another way, as I've been experimenting with in a DH2E -> Rogue Trader hack, is to offer more choices of aptitudes within those character building blocks. A given character would still have the same number of aptitudes at the end of chargen, but they'd not have to feel that they were missing out mechanically by making certain narrative decisions when choosing their homeworld/background/role.

As others have said, the aptitude system encourages specialization and adding another one won't really change that. If you want your players to freely choose options for RP reasons or whatever just have everything have a flat cost of the 1 or 2 matching aptitudes. That'd let them take whatever they want without fear of gimping their character by taking high-cost options.

It feels like DH1 is to DH2 what D&D 3.5 is to Pathfinder.

This is a really good analogy because 3.5 and Pathfinder are essentially the same game and the few quality of life improvements made in the later game do nothing to address the fundamental flaws in the game's mechanics.