In recent literature, this issue would be referenced as multiple measures placements. There's been quite a bit of work in this area in recent years, and a number of places cite positive results (in terms of shortened time to gain more credits, etc.). The displayed effect is usually stronger for English, and weaker for math. It certainly makes intuitive sense to me that using more data for decision-making ought to be more robust. However, I'm a bit suspicious of some of the findings because of ulterior motives by the institutes pushing them; usually these are joint with efforts to reduce time in school for students, reduce funding for developmental education, reduce costs for placement-testing, etc. For example, Columbia University's Teacher's College has been at the forefront of the push to end developmental classes in colleges.
Here's an overview article at Inside Higher Ed (2018). At SUNY 2016-2017 a disjunctive rule ("or") was used; students could qualify for certain classes with either a high Accuplacer score, or high school gpa (HSGPA), or state exam, or high school rank. Reported results are 14% of student were placed in a higher math course, and 41% in a higher English course. Those who did get placed higher than the placement exam would have received supplemental "corequisite" support programs throughout the semester. This resulted in 12% more students completing credit-bearing English classes in the first semester, and a 3% increase for math.
California in 2017 passed a law requiring community colleges to use multiple measures for placements. One paper supporting this was Ngo, et. al., "Course Placement In Developmental Mathematics: Do Multiple Measures Work?", USC Rosier, 2013. The practice at the time was to use a placement test as the basis, and then add or subtract some points based on survey questions and HSGPA. The overall results are broadly similar to the SUNY findings.
Note that the practice on the ground has changed rapidly between the time the OP asked this question (2014) and when I'm writing this answer (2020). For example, CUNY (where I work) has both announced the complete dissolution of developmental courses (in English, arithmetic, basic algebra, etc.), and also eliminated all system-wide placement testing. The current theory from the central university follows the SUNY practice above; any of several disjunctive criteria will qualify students for courses (SAT, or HSGPA, or state exam, or passing the class in high school, etc.). As noted, this should cut costs for placement testing and developmental education (namely, from classes that 80% of students would take to zero).
However, among the difficulties this poses is that very close to half of the students at my institution are foreign transfer students, and do not have standard high school transcripts, SAT scores, or state exams. The CUNY policy in these cases seems to promote accepting self-reported high school grades for this purpose.
Among the presentations that were distributed to us to support these decisions was one by John J. Hetts of the Educational Results Partnership (ERP), a non-profit working in this area and funded by corporate partners such as the Gates Foundation, Chevron, AT&T, etc. Hetts has a number of variations of a slide deck under the title "Let Icarus Fly"; one can be found here. This gives a glowing report in favor of multiple measures (or disjunctive measures as I'd call the SUNY/CUNY practice), quickened student time-to-credential, and reduced costs. However, some of the findings seem suspect. E.g., writing in favor of self-reported HSGPA, he writes that, "Under-reporting was 2-4X as common as over-reporting." (p. 45). But if we inspect the table on the prior page supporting this statement, we see that what under-reporting occurs is effectively negligible (e.g., in the topmost bracket, –0.04 point on average, for 1% of total GPA, N = 599), while the over-reporting is hugely significant (e.g., in the lowest bracket, +0.82 on average, or 80% of the whole GPA, N = 85). So: The students with the worst grades in high school show the highest propensity and payoff for misreporting grades to their advantage. If that wasn't an obvious outcome at the outset, one could reflect on principles such as the Dunning-Kruger effect, Campbell's Law, or the Freakonomics podcast episode on institutional-scale cheating in schools which pointed out what "school administrators were unable (or unwilling?) to foresee... when a rule change gives people incentive to behave badly, a small share of them inevitably will".
In summary: Using multiple measures for college placements (such as placement exam, high school GPA, etc.) has rapidly become widespread in recent years, and on its face should be a reasonable idea. However, the ulterior motives of the organizations pushing these findings leaves one somewhat skeptical of the very positive results that they assert (and some of the interpretations seem downright disingenuous). Moreover, the findings have been very rapidly taken up to counter-intuitively abolish all placement testing and courses like basic algebra at many large colleges. Keep in mind that even the most positive proponents show the most significant acceleration in English programs, and small or negligible accelerations in math programs.