This is long overdue and related requests have been made before.
The data for the Synoptic Problem does not change: the double and triple tradition material remain the same. It is something of an oddity that a premium software like Logos has yet to provide a solid tool that enables users to work with this material.
What we need is:
(1) An easy way to spot passages that belong to the double, triple tradition, and special materials in the text of a given Gospel. It is not sufficient to have a synopsis with parallel passages. We need something that visually gets more to the point where one does not have to scan pericopes to find the repeated material. It should be highlighted (colour-coded). The idea then is that at a glance one would be able to see where one type of material is found and to what extent.
(2) The ability to see this in synoptic layout as well. This will be needed and helpful in certain types of studies but not others.
(3) A corresponding dataset that allows users to perform searches based on these criteria.
(4) A button that allows one to see the overall "map" of a given gospel (think of it as a zoom out that allows for the whole gospel to show on the screen where text is not legible but one can see the colour outlook of the whole).
So, a browser with a side bar that allow one to select criteria that they want to show (e.g., the so-called Q material). On the right a field in which the biblical text displays with ability to select which gospels to show from 1 to 3 (perhaps even John?) and ability to choose the Bible version one works from. Corresponding selection technology could help port the highlighted text in the Greek to modern language versions that have interlinear tagging.
It would be nice to have some kind of order of material coding as well but for now I don't have a concrete idea of how this could be done. Perhaps others will. It could be something akin to the "previous context" and "next context" idea in search analyses generating a "hit" when there is correspondence between two or more gospels (i.e., a particular pericope has the same previous or next context in several gospels). This may be harder or impossible to implement, so it is just a bonus idea.
These are starting thoughts. There may be better or more practical ways of doing something like this and others may have other ideas about this.