Do you know of risks with getting a spinal block for a cesarean followed by general anesthesia for more surgery?

No: The medication used for a spinal block will usually go away within 2 hours. It does not interfere or cause problems with a general anesthetic.

Not for elective: If the general anesthetic is after the spinal has worn off then there should be no major problems. Often we use opioids in the spinal which would reduce the opioid requirements during the general. If the general anesthetic is an emergency and / or done before the spinal is worn off, you may be at risk for low blood pressure during the surgery, which is reversible by a deligent anesthesiologist.