1848 – 1852: March Revolution and a new confederation
In my opinion the best opportunity for a larger Switzerland is following the March revolutions in the Germanic countries in and after 1848.
Due to a slightly less radical program than IOTL, the revolts in Baden, Württemberg, Palatinate, Hesse and Bavaria find a large following, not just in common circles, but also in the bourgeoisie.
The efforts in Frankfurt to create a German parliament and unite the country are followed closely and when it becomes evident that the Prussian king and the other monarchs will not accept the results of the constituant assembly, the Revolution brakes out in the whole of Southern Germany
It sweeps away the Grand-Duke of Baden,the King of Württemberg, the Grand-Duke of Hesse.
The Revolution rages also in Bavaria, but the sides are even.
The deposed rulers call the Prussian-led Norddeutscher Bund for help. In the ensuing campaign, the revolutionary armies manage to beat the the Federal nothern German troops (basically the inverse result of Kandern). This tilts the scales in Bavaria, which joins the revolutionary (=liberal) states.
Prussia and its allies fear a contagion of their lands and gather large armies to quench the revolution in the South. Even tough strongly supported by arms and logistics from France, the Napoleanic experience hinders the revolutionary states to officially approach France for help. The Austrian kuk monarchy is in turmoil. But even though in Deutsch-Österreich (rougly modern-day Austria), the revolutionary forces seem to win, the other Habsburg lands are fighting the revolution and old Fürst Metternich still pulls strings behind the scenes. The last thing the revolutionary states of BWHB need is an ally where the conservative order is restored and that turns against them.
In this situation 1849, the German speaking cantons of Switzerland suggest to accept the revlutionary states of BWHB as cantons in the Helvetic Confederation. The revolution was observed in this part of Switzerland with benvolence, as it represents ideals that have been since a long time supported by the protestant cantons in the North of Switzerland.
The other Swiss cantons are appalled : revolutionaries, left bourgeois agitators that removed the old order? And the risk of a conflict with the Norddeutsche Bund under Prussia and her allies? All reform projects in Switzerland, the project of a tighter union, a central state even, are shelved under the influence of the proposal.
The Tagsatzung (the Annual meeting of cantons) of 1850 in Baden, Switzerland becomes a one-subject event. The historic inner conflicts between the cantons break open. The French, Italian and Rumantsch speaking cantons leave the assembly in protest when it becomes clear that the German speakers will not change their mind. Undisturbed by this, the German speaking cantons vote for an integration of BWHB. Even though this vote is later contested, it is formally valid as it uses an age-old loophole in the procedural rules. Not least, the Northern Swiss cantons feel safe from Prussia as the new members of the Confederation lie like a bullwark between the Northern German states and Switzerland.
For a short moment in time, the Helvetic Confederation has grown substantially.
How does it go on?
With only thinly disguised support of France, BWHB manage to repell new attacks by Prussia and its allies wishing to re-establish the god-willed order.
Deutsch-Österreich, where the revolution finally wins and establishes itself, is under mounting pressure from the other parts of the kuk empire. A coalition of Czech, Slovak, Hungarians is massively supported by Prussia and treathens to march on Vienna. Prussian troops are ready to support them logistically. In this situation, the barely established revolutionary government in Vienna reaches out to BWHB and the Helvetic Confederation. Using the same legal loophole as when BWHB joined, an agreement is ratified that assures Vienna the full support of BWHB, Zurich, Berne, Basel, Aargau, Thurgau, Sankt Gallen. Uri, Schwyz, Unterwalden, Glarus, Graubünden agree shortly after. The agreement furthermore sets out a roadmap of Austria to join the Confederation.
The Helvetic Confederation begins to split over this new breach of trust between its existing members and the still raging row on the acceptance of BWHB. Ticino is snapped up by revolutionary Italy, the French speaking cantons ask to join France under a special statute.
The now entirely German-speaking Confederation, now also containing Austria changes its name to (not decided yet).
The strong ties with France during the revolutionary phase cement the good relations, which hd already existed in the centuries before. Not to the point that the new Confederation would join the Franco-Prussian war on the side of France. After all, one speaks German, and that war remains a minor skirmish.
But the foundations and principal reasons IOTL of a catastrophic WWI are no longer given, the desasters of WWI and WWII will not happen.