Geodesic
The lattice of extensions of the modal logic of two equivalence relations has the cardinality of the continuum
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 46-48

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A continuum of different modal logics over $S5 \otimes S5$ is constructed in the paper, which proves that the capacity of the lattice of all normal extensions of the logic of two equivalence relations $\operatorname{Ext}(S5\otimes S5)$ is a continuum. 
@article{VMUMM_2011_4_a7,
     author = {M. M. Izmailov},
     title = {The lattice of extensions of the modal logic of two equivalence relations has the cardinality of the continuum},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {46--48},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a7/}
}
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M. M. Izmailov. The lattice of extensions of the modal logic of two equivalence relations has the cardinality of the continuum. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 46-48. http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a7/