A contingency table is another tool for keeping a record of the counts or percentages in a probability problem. Contingency tables are especially helpful for figuring out whether events are dependent or independent.
A two-way contingency table always shows the counts for the 4 possible combinations of events, as well as the totals for each event and its complement.
You can use two-way tables for any number of events. For a 2x2 table you get 4 cells:
e.g., A1 A2
B1 9 17
B2 11 3
You can expand this to get 3 x 2 and so forth:
e.g., A1 A2 A3
B1 9 17 7
B2 11 3 13
If using chi square you calculate the statistic in the same way, but need to compare it to a chi-square distribution with (a-1)(b-1) df (= 2 for 2x2 table).
If you have more than two dimensions you might consider other approaches such as logistic regression, Poisson regression or log-linear models.
Contingency table don't have limts of four combinations. You can go beyond 2x2 table
It is possible to construct the tables upto any limit. 2x3,3x3,4x4 and even more than that and even there is no compulsion of equal rows and columns. The only thing is number of degrees of freedom will change and we need to calculate expected values for all observed values for calculating chi-square value.
following links will help you carring out the Chi- Square analysis in Minitab and CrossTab
https://onlinecourses.science.psu.edu/stat500/node/56
http://www.psychstat.missouristate.edu/introbook/sbk28m.htm
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