There's no limit to the number of dimensions mathematically. One dimension is just another variable for some descriptions that satisfy certain conditions. Our universe needs 11 variables for a coherent mathematical description. At least we believe so for now. If you want to be a physicist, you need to be able to think mathematically, not physically. The string theory is the very example that demonstrates how physicists and mathematicians mate with each other and give birth to various freaks, which we call theories.