The pioneering company, Auticon, already employs 17 people who live with autism, the disorder characterised by difficulties with social interactions and exceptional abilities in specific fields.
SAP, which makes business software, said in May that after pilot projects in India and Ireland, it plans to employ hundreds of people with autism as software testers and programmers.
Its goal is that by 2020, people with autism will make up one percent of its worldwide workforce of 65,000.
Mueller-Remus created his far smaller company in November 2011 with the idea of "investing in the strengths" of these potential employees.
His son was diagnosed with Asperger syndrome, a variant of autism, as a teenager, and Mueller-Remus has long known that many people with autism excel in fields like programming or quality control.
"This is my talent," one of the employees, 27-year-old Melanie Altrock, stated matter of factly, sitting at her screen in a white-walled, modern top-floor office in western Berlin.
"Other people are interested in languages or math, for me it's computers. I don't just search for errors, I see them."
Auticon now has 25 staff and offices in Berlin, Munich and Duesseldorf, with plans for another in Hamburg. It looks to break even "by the end of the year", said Mueller-Remus.
"We wanted a normal consulting company, without subsidies, without donations, without funding from a foundation," he said, adding that the aim was to "combine social commitment and business".
"Today, after a little over a year, we have good customers like Vodafone, it's looking good," said Mueller-Remus.
But he also emphasised that working with autistic people can be "a very complex issue".
"We can make many mistakes because people with Asperger are very demanding people," he said.
"People with autism are very concrete, unequivocal," added Elke Seng, a "job coach" at Auticon who assists the employees in their relationships at work and with clients.
"There is no innuendo, there is only one or zero. It's rather nice," she smiled.
Friedrich Nolte, board member of the Federal Association for the Development of People with Autism, said "only five to 10 percent of people affected by autism find a place on the regular job market".
Mueller-Remus said that "their CVs often have brief episodes of work interspersed with long interruptions".
Often people with autism "have no situational awareness, may seem arrogant, have no interest in small talk, and are not interested in people because people are not logical," he said.
All of this can give rise to misunderstandings with sometimes serious consequences, he said.
In this context, the SAP initiative was widely applauded at the small company.
"That more people with autism can access a job is simply fantastic," said Seng, who confessed she finds her work "fascinating".
An autism specialist, psychiatrist Kai Vogeley of Cologne University Hospital, told a German medical journal that people with autism who work can "develop confidence in themselves".
He cautioned however that "certain conditions must be met for this to succeed".
"I hope that SAP knows how difficult it is," said Mueller-Remus. "If things are done well, you can really achieve great results."
Altrock, the autistic programmer, agreed.
"I have a full-time job, I take pleasure in it, I earn my own money and I have my own apartment," she said. "I'm glad it's like that."