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I assume by "multiple binary variable conditions" you mean something like this:

$$x_1 == 1\mathrm{\ \ AND\ \ } x_2 == 1 \implies \text{<some constraint>}$$

You can only have one indicator variable in each indicator constraint, but you can, of course, model something like the above using auxiliary variables. E.g.

$$x_3 == \mathrm{AND}(x_1, x_2)$$

and then use this new variable in the indicator constraint.