Answered by Shaykh Faraz Rabbani
Question: Is it permissible to fast every day, save for the days that it is impermissible to fast?
Answer: Walaikum assalam wa rahmatullahi wa barakatuh,
Yes, but this isn’t recommended. The maximal sunna fasting is the fasting of Prophet Dawud (peace and blessings be upon him), who fasted every other day, as the Beloved Messenger of Allah (peace & blessings be upon him & his folk) taught us. [Shurunbulali, Maraqi al-Falah; Ibn Abidin, Radd al-Muhtar]
The Messenger of Allah (peace and blessings be upon him) said that the best of fasts is the fast of Prophet Dawud (peace be upon him), who fasted every other day. [Related by Bukhari and Muslim]
Even with that fasting, one should build up to it gradually, as the sunna with works is to increase gradually; to be committed to consistency; not to overwhelm oneself by taking on too much too soon; and to focus on excellence in one’s actions, outwardly and inwardly. [Ibn `Allan, Sharh Riyad al-Salihin; Qari, Mirqat al-Mafatih]
And Allah alone gives success.