updating single row in MYSQL

We have a situation where we need to update on a single row several thousands time a second and this requirement lasts continuously for 5 hours every day due to the nature of the business. Design cannot be changed so we are looking for solutions. Usually we use very fast SSD drives for faster performance and so far we are able to cope up with the requests. But our traffic is increasing every day and we need another solution that can replace our current method and help us update same row many more thousands of time a second. Any suggestion would be great. We use MYSQL 5.6 currently