Munich has cranked up a formidable administrative machine to meet a tidal wave of refugees, taking in 18,000 exhausted human souls at its central station and getting most of them to shelter this weekend while still keeping the trains running on time.
But the region said on Sunday night that migrants were arriving faster than it could find new accommodation. It had asked the German railway operator to give it a train for them to sleep in, as well as putting up new beds elsewhere.
"It's getting tight," Christoph Hillenbrand, president of the government of Upper Bavaria, told reporters at the station, where almost 11,000 new migrants arrived on Sunday on top of 6,800 who came on Saturday.
He said a third hall at the international trade fair grounds was being taken over with 1,000 new beds, and 500 beds were being set up in a disused car showroom. Other properties could also be taken over.
Bavarian officials worked flat out through Saturday and Sunday, normally a strict day of rest in the Catholic-majority state, as train after train pulled in carrying refugees, predominantly from Syria, Afghanistan and Iraq, via Austria.
The new arrivals were medically screened, fed, watered and counted out of sight of other passengers before being transported by bus to the hastily repurposed destinations around the city, including a railway logistics centre.
Aid organisations were flooded with volunteers who erected beds and interpreted for the new arrivals, while officials scrambled for buses and drivers at the end of the holiday season and charities sorted donations into useful items.
"We coped with the World Cup, we coped with the Pope's visit, we cope with the Oktoberfest, we coped with the G7 and now we also want to cope with the current situation," Munich's administrative chief Wilfried Blume-Beyerle told reporters.
But he warned that the Bavarian capital, which has borne the brunt of arrivals in Germany since Berlin and Vienna opened their borders to migrants offloaded by Hungary, was almost stretched to its limits.
"Federal government - don't leave Munich alone!" he said. "We won't manage it on our own for much longer."
At Munich station, well-wishers turned up again to cheer the new arrivals, although, at a few dozen, they were neither as numerous nor as loud as a day earlier.
Police were highly visible, with dozens appearing on the platforms where refugees' trains pulled in to shield them from onlookers and keep them in line. But they adopted a softly-softly approach, taking an hour to persuade a train full of reluctant passengers who wanted to stay in Munich to board another train north to Dortmund.
The travellers who stopped to speak told of weeks-long journeys by land and sea. Most were young men whose friends and families had clubbed together to raise the roughly US$5,000 to US$10,000 they would need to get to Europe.
"I want to study accounting in Germany. It's my big hope," said 20-year-old Shabil from Kabul, who had travelled alone, grinning as he boarded a bus. Some of his fellow travellers seemed intimidated by the welcoming applause.
"It can be a bit off-putting. Many people are overwhelmed," said Colin Turner, spokesman for the volunteer helpers. "And it raises their hopes. It must be clearly communicated who can stay. We mustn't awaken false hopes."
About 4,000 were sent on to other German states under a 1949 agreement about cost-sharing for research institutes that has been adapted to include how to distribute asylum-seekers.
Germany's most populous state, North Rhine-Westphalia, is obliged to take the largest number of refugees this year, followed by Bavaria and Baden-Wuerttemberg in the south-west.
Bavarian officials called for more trains and buses to go directly to other states without using Munich as a staging-post - something they cannot organise alone since as a regional authority they have no say over the national rail operator.
One small group of arrivals in Munich on Sunday morning illustrated what may lie in store for thousands more once they get as far as applying for asylum.
Roughly 20 refugees from Libya, Kashmir, Bosnia, Syria and other places who had already formally applied elsewhere were taken along with their paperwork to a special counter.
Here, they were given tickets to the far-flung towns and cities assigned to administer their cases - Eisenhuettenstadt, Schweinfurt and Trier, among others - along with itineraries highlighting where they should change trains.
Some asked passers-by to show them on a map where the places were and to direct them where to go. One thought he was already in Hamburg. All had broken English at best, and no German. They made their way to the platforms unaccompanied by any officials, in family groups or alone.