You can't assign multiple Parts to the same MIDI channel unless you assign them all (except, when using Hybrid, keyboard control=OFF) Parts to the same channel. If you do this then you'll get the external control working OK but your local keys won't be able to have multiple Parts.

There is just no way to assign two different groups of MIDI channels. Meaning multiple Parts on one MIDI channel and then another set of multiple Parts on a different MIDI channel. If you could use Zone Control + Single (or Hybrid) mode, you'd have options there. However Zone control forces multi-channel so that won't work either. You'll have to find another way.

There are some options.

1) Assign keyboard to single-channel mode (there's no reason to use Hybrid here as all keyboard control=OFF Parts will not be used). The Single Transmit/Receive MIDI channel needs to match your S88's transmit channel.
2) Pick a section of your keyboard to dedicate to your S88 (external control). It can be "high" notes above the range of the notes available to you on your Montage 6 keys or below. A way to get more range on the low or high side is to also octave shift your keyboard with the OCTAVE+ or OCTAVE- buttons
3) Set the Parts you want controlled by the S88 note range (from the HOME screen) to match the range you decided on in step 2. Set the Parts you want controlled by local keys to be within the range available to you by the keys in front of you.
4) Octave shift, as necessary, your S88 so it plays notes targeting the correct range of the keyboard.

This is a note range split which will "dedicate" an area to your S88 and an area to your local keys.

-OR-

Still using single-channel MIDI mode ... You can do velocity splits where your local keys are forced to only have velocity values in some range and then force the S88 to play velocities in another range. 1-63 and the 64-127 if you could swing it. Obviously it would be easier to force all internal to one velocity and external to another velocity. Then you would velocity limit the Parts you want played by the external S88 keyboard to its velocity setting and the Parts you want played by Montage to its level. This way you could have note range overlap since the velocity is what determines which keyboard plays the given Part.

-OR-

Invest in something that goes between your S88 and Montage that can take the single MIDI channel output by the S88 and replicate this to multiple channels of your choice. You would have Montage in multi-channel MIDI mode in this case (or Hybrid and target Parts 9-16 for your S88 channels. Camelot Pro is software you can use to do this so a laptop/PC or tablet would need to be between MIDI connected to both the S88 and the Montage (using USB to Host port on Montage - so use USB mode). There are other options of what can go between. This would make up for the deficiency of not being able to assign MIDI input channels arbitrarily to any Montage Part.

The S88 doesn't allow for overlapping key zones. So although it has 16 zones available that they cannot overlap means you cannot use this feature as a way to send to multiple MIDI channels at once from the S88.

-OR- least favorable I'm sure ... (pick a different MIDI controller)

The Novation SL MK3 controllers only have 8 zones but allow for overlapping of zones. Therefore, this MIDI controller can handle communicating properly with Montage in Multi-Channel mode without having to have a device between to retarget the MIDI channels. That doesn't help you necessarily - but this is why I have a Native Instruments MIDI controller collecting dust (with 16 zones) while the Novation is not.

the Komplete Kontrol S88 is a multi-zone controller (I believe you can split the keyboard into as many as 16 zones, which can overlap as little or as much as you want). So instead of your goal being "Parts 1-4 go on Midi channel 1 instead 1-2-3-4" just set your S88 to transmit on 1-2-3-4.

For other reasons, you might prefer to leave those lower numbered Parts/Channels set for sounds to be played by the internal keys of the Montage, and use higher number Parts for the ones you want to trigger externally from your S88, but that's another conversation.

The manual claims you can't overlap. Was there a midstream update to the firmware to allow for overlapping zones?

Source: https://www.native-instruments.com/fileadmin/ni_media/downloads/manuals/komplete_kontrol/KOMPLETE_KONTROL_S-Series_MK2_Manual_English_04_2022.pdf Page 79:

10.7.1. About Key Zones
...
Key Zones span the entire range of MIDI notes. You can have between 1 and 16 Key Zones. Key
Zones cannot overlap (i.e. each key can only belong to one single Key Zone), and they cannot
have gaps between them (i.e. each key must belong to a Key Zone). You can disable particular
Key Zones: in this case their keys will not send any MIDI Note message (dead keys).

The S series latest firmware is from 2109 prior to the publishing date of this manual.

Thanks for the correction, Jason, I somehow missed that. Bummer. I can see why overlapping zones could have been a design issue for them, since it could be seen as interfering with the ability to have each sound/zone represented by its own dedicated LED, which is a key selling point. Though I could imagine an implementation where simply a single zone/color can have multiple MIDI channels assigned to it.

The Novation has the "same" per key LED and yet supports overlapping zones (although only 8, not 16). I have an NI S-series MIDI controller and really didn't realize (until now) you cannot overlap zones. The reason why I jumped ship is that the NI doesn't function very well standalone and requires a computer of some sort running their Komplete Kontrol software to really utilize its capabilities and only a very limited "dumb" mode without the computer. You can't even load up profiles using the computer then use those profiles apart from the computer. So the NI didn't fit within my usage needs outside of this overlapping behavior.

I think had my usage been more in-the-studio vs live use I may have been able to live with tying it to a PC (since in the studio the keyboard is mostly plugged into one) but this inability to overlap zones would have not worked out well and finally realized when trying to layer externally.