So, I've got only ONE active bass in my arsenal and honestly am not too to knowledgable in the world of active basses. 4 years ago I won a 5 string Dimension Deluxe with dual pickups that I love ALMOST to bits....almost. Thing is, I want to be able to cut ALL top end off from time to time and no matter how much I boost the bass and cut the treble and mids on the onboard pre-amp, there is still some pretty clear treble going on when I just want straight rumble. Is this just a plain active occurance? Or just a cheap {it is a MIM after all} pre-amp that should be upgraded? ADDITIONALLY is there a way to get it modded to active/passive while maintaining its suuuuuper weird {but weirdly tasty} pickup selection configuration.
 
I think the issue your experiencing with treble bleeding through the actual Treble Cut in the preamp could be due to a poor match of frequencies between the preamp an pickup. But I don’t know enough to go into details or if I am even correct in this thinking.

From reading a bunch on the things users don’t like about the Dimension, the preamp seems to be a big part of it.

Here is a very good write up regarding a USA Dimension and preamp swap:
Fender American Deluxe Dimension HH IV with Audere Pro Z Pre-Amp
 
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Active preamps are designed to have a certain frequency range for each control, as well as a max boost and cut for each control. Sounds like you are just not happy with the max cut for mids and treble. This isn't really because that preamp is "cheap" or lower quality, it's just a design decision that's made at the time the electronics are designed. It might seem stupid to limit the min/max range of the control - more is better, right? But there's a tradeoff - controls with very large boost/cut ranges tend to be very very sensitive (a small tweak of the pot makes a huge difference in the tone) which can be incredibly frustrating.

That said, it's pretty trivial to add a passive tone control, either on the output of the preamp or on the input (between the pickups and the preamp). Just a normal old pot with a normal old cap. If you put it on the input side, you can use typical tone control values (250k or 500k pot, .047-ish cap). If you put it on the output, you need to scale up - 25k pot and .1uF cap would be typical. Adding this control leaves you with an "active" bass, but gives you an extra degree of treble cut. Personally, I'm a big fan of this, though I typically leave the passive tone control in the control cavity, as a mini trim pot, and use it to set a "baseline" tone. Then I use the active tone control on the EQ to tweak from there. But you can have the new tone control on the outside of the bass like all the other pots if you want.

That change can be made independent of installing an active/passive switch. An active/passive switch can be added also but it's hard to speak to how to do so without knowing more about the preamp. If you can show us photos we can probably figure it out. (unless someone comes along who knows that preamp well enough).
 
Thank you guys for the informative responses! I’ll definitely check into how to get both accomplished! The idea for passive mode would definitely be a switch and Concentric Pots on the treble {Similar to the Am Ultras} with one knob being treble and the other just Tone.
 
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Thank you guys for the informative responses! I’ll definitely check into how to get both accomplished! The idea for passive mode would definitely be a switch and Concentric Pots on the treble {Similar to the Am Ultras} with one knob being treble and the other just Tone.
That's not easily done on the Dimension. The preamp is a big circuit board with the pots and switching all attached to it. I'm talking major circuit mods. Even the output jack is a very complicated thing, not the usual TRS usually found in active instruments. I have a single H MIM Deluxe Dimension that had a bad mid pot, below average treble and volume controls and loose output jack. Trying to find replacement pots and jack was a no go. I eventually found a NOS preamp. It was an easy swap, but it still does the Dimension thing--which is a more mid forward and darker tonality relative to a Stingray. I do find that if I boost the bass, cut the highs and mids, it's fairly rumbly, for that particular bass, which is really designed to be more punchy.
It would behoove you to do one of a couple things:
1. Just swap out the whole preamp with something that would give you active/passive & passive tone control and then figure out how to wire a new pickup switch to it. This would be semi-complicated, especially the switch wiring.
2. Use some sort of graphic/parametric EQ or LPF pedal to give you that straight rumble. Super easy, no mods necessary.