In 1995, Robert Thomason published “Symmetric monoidal categories model all connective spectra” in TAC. On page 2, he argues that symmetric monoidal categories are more convenient than “May’s coordinate-free spectra” for various reasons, one of which is that a symmetric monoidal structure is easier to obtain (this was before EKMM or the Hovey-Shipley-Smith paper on symmetric spectra). Thomason writes:



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> As convincing evidence for this claim, I refer to my talk at the Colloque en l’honneur de Michel Zisman at l’Universite Paris VII in June 1993. There I used this alternate model of stable homotopy to give the first known construction of a smash product which is associative and commutative up to coherent natural isomorphism in the model category. This will be the subject of an article to appear.
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Unfortunately, he died later that year. Hence my question:



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> Did anyone ever work out the construction of the smash product he had in mind?
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Status of Thomason's idea for a symmetric monoidal model of stable homotopy - from his last paper
I think that the best thing in this direction is the paper "Permutative categories, multicategories and algebraic K-theory" by Elmendorff and Mandell. 


I have only skimmed this so I may well not be understanding it correctly. 


Anyway, we want to consider symmetric monoidal categories, whose monoidal structure should be thought of as "addition", so I will call them "plus-monoidal categories". We want to define a kind of tensor product of plus-monoidal categories. Elmendorff and Mandell say that we should first generalise and consider plus-multicategories. We can then define multilinear functors between plus-multicategories (as at <https://ncatlab.org/nlab/show/multicategory>), making the class of plus-multicategories into a tensor-multicategory. One can then show that there are universal multilinear functors in a suitable sense, so we can form tensor products of plus-multicategories as desired.


