Question: Which has more locations, the California Institute of Technology or the University of Illinois system?

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Edward McCaffery: Edward McCaffery (born c. 1958) is a tax law professor at the University of Southern California Law School and also a visiting professor of Law and Economics at the California Institute of Technology.  At USC he is Robert C. Packard Trustee Chair in Law and Professor of Law, Economics and Political Science.  He teaches Federal Income Taxation, Property, Intellectual Property, and Tax Law and Policy at USC, Law and Economics and Law and Technology at the California Institute of Technology.  He also teaches Corporate Taxation, Federal Income Taxation, Partnership Taxation, Property and a Tax Policy seminar.

University of Illinois at Urbana–Champaign: The University of Illinois at Urbana–Champaign (also known as U of I, Illinois, or colloquially as the University of Illinois or UIUC) is a public research university in the U.S. state of Illinois.  Founded in 1867 as a land-grant institution in the twin cities of Champaign and Urbana, it is the flagship campus of the University of Illinois system and a founding member of the Big Ten Conference.

California Institute of Technology: The California Institute of Technology (abbreviated Caltech) is a private doctorate-granting university located in Pasadena, California, United States.

Naomi B. Lynn: Naomi Burgos Lynn (born 1933) was the first Hispanic woman president of an American public university.  She served as President of Sangamon State University in Springfield, Illinois, beginning in 1991 and through its entrance into the University of Illinois system as the University of Illinois at Springfield.  She retired as Chancellor of UIS in 2001.  At her retirement the Naomi B. Lynn Distinguished Chair for Lincoln Studies was created at the University of Illinois at Springfield, where Dr. Phillip Paludan served as its first recipient.

Roy Dow: Roy Dow (born May 2, 1962) is the former head coach of the NCAA Division ll Pfeiffer University women's basketball program in Misenheimer, North Carolina.  Previously, Dow was the head coach at California Lutheran University, where he was at the helm from 2008-2013.  He led the women's program (Regals) to an 81-51 record, two conference championships and two NCAA tournament appearances.  Dow is third all-time in wins at Cal Lu (81) and second all-time in win percentage (.610).  Dow was also the head coach of men's basketball at the California Institute of Technology.  He coached at Cal Tech for six years (2002-2008).  Dow appeared in the documentary Quantum Hoops, a 2007 film directed by Rick Greenwald, that follows the California Institute of Technology's basketball team—the Caltech Beavers—in their attempts to end a 21-year losing streak during the final week of the 2006 basketball season.  The documentary premiered on January 26 at the 2007 Santa Barbara International Film Festival, where it won a Top 10 Audience Choice Award.  It first screened in theaters on November 2, 2007 in Pasadena, California, and was featured at the 30th Denver Film Festival on November 8.

University of Illinois Press: The University of Illinois Press (UIP) is a major American university press and is part of the University of Illinois system.  Founded in 1918, the press publishes some 120 new books each year, plus 33 scholarly journals, and several electronic projects.  Strengths include ethnic and multicultural studies, Lincoln and Illinois history, and the large and diverse series "Music in American Life."

University of Illinois at Chicago: The University of Illinois at Chicago or UIC is a state-funded public research-intensive university located in Chicago, Illinois, United States.  Its campus is in the Near West Side community area, adjacent to the Chicago Loop.  The second campus established under the University of Illinois system, UIC is also the largest university in the Chicago area, having approximately 29,000 students enrolled in 15 colleges.

William Andrew Goddard III: William Andrew Goddard III (born March 29, 1937 in El Centro, California, U.S.) is the Charles and Mary Ferkel Professor of Chemistry and Applied Physics, and Director, Materials and Process Simulation Center at the California Institute of Technology.  He obtained his B.S. from the University of California, Los Angeles, in 1960 and his Ph.D. from the California Institute of Technology, 1965.  After his Ph.D. he remained at the California Institute of Technology as Arthur Amos Noyes Research Fellow (1964–66), Professor of Theoretical Chemistry (1967–78) and Professor of Chemistry & Applied Physics (1978-).

University of Illinois system: The University of Illinois System of universities comprises three universities in the U.S. state of Illinois: Urbana–Champaign, Chicago, and Springfield.  The university in Urbana–Champaign is known as "Illinois", "U of I", or “UIUC”, whereas the Chicago campus is known as “UIC” and the Springfield campus as "UIS."

University of Illinois at Springfield: The University of Illinois at Springfield (UIS) is a public university in Springfield, Illinois, United States.  The university was established in 1969 as Sangamon State University by the Illinois General Assembly and became a part of the University of Illinois system on July 1, 1995.  As a public liberal arts college, and the newest campus in the University of Illinois system, UIS is a member of the Council of Public Liberal Arts Colleges.  UIS is also part of the American Association of State Colleges and Universities and the American Council on Education.  The campus' main repository, Brookens Library, holds a collection of nearly 800,000 books and serials- in addition to accessible resources at the University of Illinois at Chicago and University of Illinois at Urbana-Champaign campuses.

Supporting paragraphs: California Institute of Technology University of Illinois system
Answer: University of Illinois System