California State University turned away more qualified applicants than ever last year — 1 in 10 students, or 31,000 people — even though the state’s Master Plan for Higher Education says they should be admitted.

Now, as CSU prepares for disappointment at the 3 percent funding increase Gov. Jerry Brown is expected to propose Wednesday for the university’s 2018-19 budget, university officials say that while money is critical, even a higher allocation would not immediately give the 23-campus system enough room for all the students who qualify.

“The last thing we want to do is admit students who we can’t provide with classes and services,” CSU spokesman Mike Uhlenkamp said.

Only six of the 23 CSU campuses have enough room to accommodate all qualified freshmen, while just seven can take all qualified transfer students. Meanwhile, state Education Department records show that the number of high school graduates who qualify for CSU has more than doubled in the past 20 years, to 194,689 students from 96,879. CSU applications are also on the rise.

The state’s higher education master plan directs CSU to admit the top one-third of all graduating high school seniors. But figuring out where to put everyone — and making sure they get a good education, said Uhlenkamp — is a math problem that goes beyond money and gets to where students are willing to live and how many years it takes them to graduate.

Yet, as the state’s budget-battle season officially opens Wednesday, with Brown presenting his proposed 2018-19 budget for every agency, the timing is perfect for CSU faculty leaders to take aim at the state for what they say is years of fiscal starvation.

“The lack of capacity on campuses is due to the 30 years’ lack of funding,” said Jennifer Eagan, president of the California Faculty Association, which represents CSU instructors.

On Wednesday, faculty members are preparing a bit of pop-up theatrics called “Every Student Deserves a Seat — Fund the CSU!” on the north lawn of the state Capitol building in Sacramento.

Faculty leaders plan to set up 1,570 chairs, each representing “the missing seats for 20 qualified students turned away from the CSU in the 2016-17 academic year,” according to a statement released by the union. Red-vested faculty members will play the part of docents for the “art installation” and talk with anyone who wants to hear more about CSU’s budget woes.

CSU’s total allocation from the state is typically about $6 billion a year. The union says CSU needs an increase of $423 million for next year.

CSU is asking for an increase of $283 million — which officials say would let them admit another 4,300 students next fall. The university also expects to raise revenue with a tuition increase that trustees would approve in March.

Brown is expected to allocate an increase of $122 million.

“In the absence of adequate, sustained and predictable funding from the state, CSU enrollments cannot keep pace with the demand from new students,” said Vincent Cevasco, a researcher with the California Faculty Association.

But CSU, prodded by the state, will soon try some methods other than more state funding to reduce the number of “denied eligibles” — applicants who qualify yet are rejected, typically 20,000 to 30,000 a year and growing.

One method is a strong effort to get more students to graduate in four to six years, in part by eliminating remedial classes for students who are poorly prepared in math or English. The elimination of those classes, which don’t count toward graduation, is to begin next fall. Instructors will be expected to find ways of helping such students along in regular classes, and many faculty are not happy about it.

Another approach is to more closely emulate the University of California’s admission system. UC admits every qualified applicant — but not always to the campus of their choice — while CSU turns down applicants rather than tell them that they can attend a campus that has room.

That may change.

The state budget approved in June requires CSU to present the trustees in March with ideas for a UC-like admission system. The deadline for approval is in May, with implementation for the 2019-20 academic year.

The problem for CSU, said Uhlenkamp, is that “a lot of our students are place-bound. They live at home, and they’re not going to uproot themselves and go to Cal State Bakersfield, or Dominguez Hills.”

Across all campuses, however, CSU has only enough campus housing for 15 to 20 percent of students, Uhlenkamp said. As for building another campus, Uhlenkamp chuckled.

“People talk about building one in Stockton or Chula Vista,” he said. “Would students go there?”

Nanette Asimov is a San Francisco Chronicle staff writer. Email: nasimov@sfchronicle.com Twitter: @NanetteAsimov