Hi my friend,
Let me clarify a few things.
1. You just bought a SE846.
2. You want a quality DAP.
3. You've heard a lot of positive reviews of the Fiio X3 and it is quite value for money.
4. You're curious if it will work with headphones.
5. You're wondering if we have any other DAPs to suggest to you.
So, if my understanding is correct, then I'll need a little bit more information from you regarding what kind of headphones you're looking at. The X3 has no issue driving the UE6000 and Sennheiser Momentums, but it will really fall flat if you try to make it drive the HE-500.
The SE846 will be drive quite decently by the X3, but IMO it scales with more power so something like the iBasso DX50 will be slightly better since it has a gain switch.
Most IEMs are quite efficient and can be easily driven by most sources. It is just that the high end IEMs really do benefit from having additional power and this is especially true when you start to look at CIEMs.
I'm just curious, have you bought the X3 or are you looking at buying the X3? If you are looking at the X3, then may I ask what are you using the 846 with right now?