I think I should clarify. I wasn't referring to Severus campaigning against the Marcomanni or any of the groups along Rome's Danubian German frontier.
Danubian Germania is where a campaign of Septimus would make the most sense, mostly because it was a region that prooved to be more troublesome than Rhineish Germania at the point, mostly due to being under direct pressure of inner movements.
A campaign in the direction of the Weser or Main in the early IIIrd century makes, strategically, little sense : the region is calm, and would remain so without a PoD in Central Europe.
At best, you could have an earlier troubled Upper Danube, over Raetian borders, as it happened in the early reign of Caracalla (altough the reason for campaigning against Allemani remains unclear), but Rhine simply stopped to be a main strategical concern for Rome since decades n the 200's/210's.
An expedition there would be, as said SlyDessertFox mostly for the sake of expension, or as I'd like to say, for the lulz of it. While less of a concern for Rome, the region directly neighbouring the imperial provinces were a good poll of auxiliaries and laeti, as point the archeological finds about Allemani.
I was more referring to an attempt to expand Roman rule from the Rhine to the Weser, and fortifying the region from the bottom of the Weser to the fortifications in Germania Superior.
You'd have more chances on that with a PoD before Antonines, as with their rule, the military focus clearly shifted on Danube and Persia. Either with a longer rule of Domitian, or a smoother succession, but another campaign against Chatti seems to me the latest plausible PoD avaible for a, modest, expansion of Rome on the Weser/Main basins.
The reasons for this are that it would bring the Romans into contact with the Lombards and Saxons, on the far side of the river, and perhaps with some luck forestall their later rise, all the while enriching the Empire with the spoils of a successful conquest of the Frisii, Chauci, and what would later become the Alemanni.
Lombards would be a really secondary people by the Ist century, being dominated by Marcomanni (and as such already in contact with Rome).
Saxons, however, didn't yet appeared as a distinct confederation : peoples that formed it probably already existed tough.
Alemanni, on contrary, seem to have already emerged as a confederation in the lower Rhine basin : moreover, they were largely present within Germania Superior in the early IIIrd century, essentially romanized people.
I don't see why you think Rome would be interested on conquering Frisii and Chaucii, eventually. As said above, the usual strategical objective of Romans was to beat peripherical into submission, crush their numbers by deporting prisoners well into provinces, enroll the others as auxiliaries (as Usipians in Caledonia) and enact some clear proofs of suzerainty.
I think you're underestimating the level of integration of Germanic chiefdoms and confederacies : most of these didn't grew out of themselves, but as you pointed in your OP, did exist because Rome, well, was a thing and not only influenced them culturally, but had a sorta working relationship with bordering polities. The modus vivendi between Rome and Germans (that, again, were largely present in the western provinces as laeti and auxiliaries) wasn't just coincidental, but was institutionalized by Romans themselves (which then helped structurte Germanic complex chiefdoms) : to throw out this institutionalized relationship would ask for more than just "we want to get direct contact with people we have already have contact with".
On this regard, a deeper expedition against Chatti in the late Ist century would be a good motivation and a plausible PoD, if Domitian survives, to have extended Agri Decumati on Weser/Main basins.
Agri Decumates would be lost in the chaos of the 3rd Century Crisis, but with such an expedition, this might be avoided by pushing the frontier up and bringing the tribes that would be an issue later on under Roman direct rule.
Again, most of neighbouring peoples were either clientelized or integrated within Germania Superior or Inferior as laeti, auxiliaries or even some equivalent of foederati. For all it's worth, Alemanni were partially under Roman direct rule, in the Agri Decumati : their confederation is more or less tied to this political fact.
It's what make me doubt that extended Agri Decumati could hold the IIIrd century crisis : because Barbarians were an integral part of it, demographically and politically.
At worst, you'd end up having them forming a different confederation or league than Franks with Upper Rheinish and/or Danubian peoples instead of Lower Rheinish peoples.
At best, you'd end up having Alemanni on steroids which could make Agri Decumati turning more like a
foedus, rather than just giving up on it, and maybe make Alemanni playing the role of Franks ITTL, as relatively trusted federates.
There would really be no benefit in trying to establish Roman rule in the Danubian regions of Germania, as it would upend imperial diplomacy with the tribes there and create more indefensible borders without real reasoning or benefits behind it.
I entierly agree : but that's as well the case of Rheinish borders. If anything, the relation between Romans and Germans there was even stabler due to less pressure from migrating groups in the late IInd century.
You'd even have more incitative, with a PoD during Septimus' reign, to have an expedition in Danubian Germania because most of the troubles happened there and that it wouldn't be far-fetched to have some of them happening in the 200's/210's. On contrast of Rhineland Germania that didn't knew such kind of pressure at this point and not before some decades.
The areas that Augustus tried and failed to bring into the Empire are essentially what I had in mind.
It's not really clear what Augustus attempted to take, and I rather think he had no clear idea either. While Romans certainly set up a direct rule as far as Dortmund, what existed beyond a line going (roughly) from Munster to Wruzburg looked a lot the relation ship that existed between Rome and Sequani earlier, as in a sort of alliance/clientelization, than a provincialisation : the lack of clear geographical or political limits certainly helped the confusion.
Not that a Roman control of part of Germania beyond the Rhine is unthinkable : but it would be relatively hard comparatively to the few advantages, economical or strategical (altough, as SlyDessertFox pointed, it could serve as a political victory).
Augustus had something that Domitian didn't have tough : in the Ist BCE, Germania was a big unknown for Romans, and disrupting the local political balances had less impact that it had one century later. Rome at some point needed as much a stable relation with Rhineish polities than these depended from it.
In a really short attempt to illustrate the possibilities...(sorry for Frisia, BTW, I'm still finishing the overall map)
1) Situation in the IInd century
2) What Domitian could realistically expect from an extended Agri Decumati
3) What Romans effectively controlled, roughly, in the Ist century BCE.
This would put the Romans in control of the North Sea coast up to the Weser, which would offer North Sea trading opportunities (as well as more coast for the Navy to defend against raids, unfortunately).
Rome was already pretty much in contact with North Sea trade ensemble, it's more or less why they went for Britain IOTL.
As for maritime raiding, the point is not they needed more coast (especially coasts than like in Frisia, were particularly swampy and unfit the development of coastal fleet, not without massive development that even Britain didn't have IOTL), it's that IIIrd century Romania couldn't afford it being stuck in a loop of coups, raids, raids and coups.