Okay, here's a couple suggestions you might try with your current setup-
1) You can use a pair of Mid/Side encode/decoders to change the effective stereo width of the 120 degree X/Y Beyer microphone, essentially making the inclusive angle narrower or wider than 120 degrees. To do so with two Mid/Side instances, you'd first convert the Left/Right stereo signal back to Mid/Side, make the adjustment to the M/S ratio, then convert back to L/R again. Or you can use a stereo-width adjustment tool which is basically doing the same in a single step.
My suggestion is to play with making the Beyer mic contribution wider than 120 degrees. On its own that will probably sound less focused and more reverberant (not what you'd want if making the recording using that microphone alone), but in combination with the center shotgun that will give you greater differentiation between front focus and immersive width. You'll probably want to readjust the M/S ratio of the stereo shotgun, likely making it a tad wider, to get the best blend and to get a bit more of the sharp coincident imaging across the front.
If you want to play around with taking the mixing to the next level using EQ, you already have lots of additional options available to you with this arrangement. Besides general EQ of the resulting stereo mixdown, you can EQ each pair separately, making each sound its best for the sonic attributes it is contributing. You can EQ the center shotgun for clarity and the X/Y ambient pair for smooth naturalness, or whatever works best. You can even push that a bit, trying different curves which compensate one pair against the other such that the overall EQ remains the same, but the emphasis within the overall sonic scene is altered one way or another. Each pair listened to in isolation may sound less than optimal that way, but it balances out when combined. Best to start with simply making each pair sound best on its own in isolation prior to combining them, before going to far with those kinds of compensating EQs.
You can go deeper than that, and play with EQing the Mid and Side signals of each pair differently. This provides control over the stereo width of each pair by frequency range. Say you boost the low frequencies of the Side signal while reducing the same frequencies in the Mid signal by the same amount. The L/R stereo output will have the same overall EQ balance as before, but the stereo width at low frequencies will be widened while the stereo width at mid and high frequencies remains unchanged. This technique is powerful and can be applied to to any stereo recording by converting it to Mid/Side and back as described above.
2) Try pointing your Beyer X/Y microphone backwards instead of forwards. This sounds crazy but its really a further extension of making the ambient collection portion more differentiated from the front focused part. It is also likely to make the ambient portion sound wider and more immersive and will provide additional control over the direct/reverberant balance of the recording by adjusting the relative levels of the two. As above you may want to use a bit more stereo width from the M/S stereo shotgun in combination with doing this, but perhaps not. Best to decide that kind of thing by listening as those choices will vary given the recording situation. Note that you'll want to route the Left channel to Right and Right channel to Left if pointing your Beyer stereo microphone backwards, or probably easier to simply rotate the microphone so that it is upside down when pointing backwards so that the Left capsule side is still pointing Left, and vice-versa.
Other things to try with all this in mind-
If you have a pair of cardioids and want to try using them instead of the Beyer X/Y mic for the ambient portion of the recording, try using those near-spaced (easier to setup than wider spaced omnis) but pointed 180 degrees away from each other to each side instead of forward. Again, probably not what you'd want if using that pair alone, but more optimal for combination with the forward facing stereo shotgun. Push them apart as wide as is practical for a single stand and whatever mic bar you are using. A good target would be twice the width of a standard near-spaced arrangement if you can manage that. With regards to the microphones forming a single multichannel stereo array, think of the of the center shotgun and each cardioid as forming adjacent near-spaced pairs with a 90 degrees inclusive angle, which is why twice the spacing of a standard near-spaced cardioid pair is probably a good starting point if you can manage that.