Unemployment benefits in the United States did not only support recession struck individuals, create opportunities for volunteerism, and had covered their expenses, but also cause minimum wage employees to quit their jobs.
A. Unemployment benefits in the United States did not only support recession struck individuals, create opportunities for volunteerism, and had covered their expenses, but also -> support, create and had covered are not parallel. Incorrect.
B. Unemployment benefits in the United States not only supported recession struck individuals, created opportunities for volunteerism, and covered the expenses of the unemployed, but also -> supported, created and covered are parallel. Let's read further "not only supported.... but also cause..." is not parallel. Incorrect.
C. Unemployment benefits in the United States did not only support recession struck individuals, create opportunities for volunteerism, and cover the expenses of the unemployed, but also -> This is better. Let's keep it.
D. Unemployment benefits in the United States supported not only recession struck individuals, create opportunities for volunteerism, and cover their expenses, but also they -> "supported not only...but also cause" is incorrect structure. Incorrect.
E. Unemployment benefits in the United States did not only support recession struck individuals, create opportunities for volunteerism, and cover their expenses, at the same time -> not only ....at the same time is incorrect idiom structure. Incorrect.
So, I think C.