What is the ruling on continuing to observe voluntary fasts after having fasted to make up for missed days and observed the six days of Shawwal?

There is no harm in connecting a voluntary fast with a make-up fast or with the six days of Shawwal. It is permissible to continue voluntary fasting after completing the six days of Shawwal, as long as it does not lead to harm or the neglect of rights. However, the best guidance is not to complete a full month of fasting other than Ramadan (definition), and to alternate between fasting and breaking the fast, as the Prophet, peace and blessings be upon him, used to do. As for perpetual fasting (fasting the entire year except for the two Eids and the Days of Tashreeq), it is disliked by scholars.