I know they changed the way you multiclass to feat-based, but is there any way to start with two classes and level them both at the same time like the gestalt rules for dnd 3.5?
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Besides the feat-based multiclass system, Players Handbook 3 introduced the concept of hybrid characters, where you pick two classes and take features from each (class features, abilities, powers, feats, bonuses to defenses, etc.). However, this is somewhat limited:
Essentially, though, you'll need the PH3 or the Character Builder app to see what you get from each hybrid class you pick, and (as usual) the Character Builder will help a great deal in keeping track of it all. Also, the Hybrid rules section includes the caveat that you may end up with a character that isn't as effective as a single-class character designed to fill one of DnD4e's four roles (defender, controller, etc.), given that you won't start with all the class features that help your character do their "job," so to speak.
That being said, in the game I'm running, I have a player who made a hybrid rogue/warlord, and while he has to sometimes get creative in terms of how he approaches combat, I think he does as well as anyone else.
This blog post helped refresh my memory since I didn't have the PH3 in front of me: http://brokenrpg.com/2010/03/16/dd-4th-ed-hybrid-characters/
Addressing the question form another angle... no: as far as I know there are no official rule for building a party of gestalt (read: a combination of two classes that is more powerful than standard) characters.
As already and clearly pointed out by @Jason S., hybrid characters are designed to be in line with "standard" ones (and PH3 also states that some combinations could also be underpowered).
Check out the Hybrid rules in the Player's Handbook 3.
You do get both classes leveling at the same time, but each is about half strength as opposed to D&D 3.5's full strength.
Here is a pointer to the Hybrid Cleric for an example, if you have DDI access.