Weinberg warned against interpreting the term "second quantization" too literally, and the term "third quantization" has been used as a misnomer in quantum cosmology and string theory. However there has been some speculative research into the idea of multiple quantiization. In particluar Carl von Weizsacker proposed a theory of multiple quantisation in the 1950s starting with one bit, or "ur" as he called it. By repreated quantisation he hoped to build a complete theory of the universe. While unsucessful, his ideas are still seen as forerunners to ideas about qubits and the role of information in physics. It is less well known that Yoichiro Nambu had written about thrid quantisation even earlier.

More recently the idea has been explored in the context of string theory and n-category theory. Here is a list of references:

P. Gibbs, "An Acataleptic Universe" http://fqxi.org/community/forum/topic/1603

M. Kober, "Quantum Theory of Ur Objects and General Relativity", arXiv:0905.3828

L. Motl. "Quantum Graphity" in "the reference frame (blog)" (2006) http://motls.blogspot.com/2006/11/quantum-graphity.html

L. Motl. "Evaluating extreme approaches to the theory of everything" in "the reference frame (blog)" (2006) http://motls.blogspot.com/2006/07/evaluating-extreme-approaches-to.html

D. R. Finkelstein, "General quantization", quant-ph/0601002

L. Motl, "Measuring the depth of ideas" in "the reference frame (blog)" (2005) http://motls.blogspot.com/2005/07/measuring-depth-of-ideas.html

D. Graudenz "Multiple quantization in Fock space" In Castell, L. (ed.) et al.: Time, quantum and information, 355-360 (2003)

K-G Schlesinger "On the universality of string theory", Found.Phys.Lett. 15 (2002) 523-536, hep-th/0008217

J. Baez, "The Story of Nth Quantization" (2001) http://math.ucr.edu/home/baez/nth_quantization.html

P. Gibbs, "Event symmetric space-time", Weburbia press,(1998) http://www.weburbia.com/press/esst.htm

K-G Schlesinger "Towards Quantum Mathematics Part II: Manifold Notions", (1998)

K-G Schlesinger "Towards Quantum Mathematics Part I: From Quantum Set Theory to Universal Quantum Mechanics", (1998)

P. Gibbs, "Event Symmetry for Superstrings.", Int.J.Theor.Phys.37:1243-1252,(1998)

D. R. Finkelstein, "Quantum Relativity", Heidelberg: Springer, (1996)

H. Lyre, "Multiple quantization and the concept of information", Int.J.Theor.Phys.35:2219-2225, (1996), quant-ph/9702047

P. Gibbs, "Superstring partons and multiple quantization", (1996), hep-th/9609118

P. Gibbs, "Is the universe uniquely determined by invariance under quantization?", (1996), hep-th/9603165

H. Lyre, "The Quantum theory of Ur objects as a theory of information", Int.J.Theor.Phys.34:1541-1552, (1995)

L. Crane, "Clock and Category; IS QUANTUM GRAVITY ALGEBRAIC", gr-qc/9504038

L. Crane, I. B. Frenkel, "Four dimensional topological quantum field theory, Hopf categories, and the canonical bases", hep-th/9405183

T Görnitz, D Graudenz, CF v Weizsäcker "Quantum field theory of binary alternatives", International Journal of Theoretical Physics, (1992)

M. Srednicki, "Infinite Quantization", UCSB-TH-88-07, Jul (1988)

M. B. Green "World sheets for world sheets", Nucl. Phys. B293 (1987), 593-611

C. F. von Weizsäcker "Probability and Quantum Mechanics", Br. J. Phil. Sci. 24,321 (1973).

C. F. von Weizsäcker "Die Quantentheorie der einfachen Alternative (Komplementarität und Logik II)", Zeitschrift fur Naturforschung, 13a:245-253 (1958)

C. F. von Weizsäcker "Komplementarität und Logik", Die Naturwissenschaften, Zeitschrift fur Physik, 60:573-586 (1955)

A. E. Scheidegger "Multiple Quantization", Canadian Journal of Physics, V,1 p26 (1953)

Y. Nambu "Second Configuration Space and Third Quantization", Progress of theoretical physics, (1949)

Y. Nambu "On the Method of the Third Quantization ", Progress of theoretical physics, (1949)