As a general rule, how many specific substrates can bind to an enzyme?
There is no general rule.
The simplest possible case would be an enzyme that simply converts one molecule into another molecule by changing which atoms in the molecule are bonded to each other. One substrate molecule binds, the enzyme breaks/makes a few bonds and releases one product molecule.
Anything is fair in enzyme catalysis.
Some enzymes bind two separate substrates, bind them to each other, then release one product molecule. Some enzymes bind two separate substrates and convert them to two totally different products.
Some enzymes need to bind non-substrate molecules - that is, molecules which affect how the enzyme functions, but aren't themselves converted from substrates to products in the reaction.