Yes, it is permissible to make up missed Ramadaan fasts on the day of doubt and one or two days before Ramadaan.
It was proven that the Prophet (peace and blessings of Allaah be upon him) forbade fasting the day of doubt, and he forbade anticipating Ramadaan by fasting one or two days before it begins, but this prohibition does not apply to a person who has a habitual pattern of fasting, because the Prophet (peace and blessings of Allaah be upon him) said: Do not anticipate Ramadaan by fasting one or two days before it begins, but if a man habitually fasts, then let him fast. Narrated by al-Bukhaari, 1914; Muslim, 1082. So if a person is used to fasting on Mondays, for example, and that coincides with the last day of Sha'baan, then it is permissible for him to observe that as a voluntary fast and it is not forbidden for him to do so.
If it is permissible to observe a voluntary fast that one does regularly, then it is more appropriate that it should be permissible to make up a missed Ramadaan fast, because that is obligatory, and because it is not permissible to delay making up missed fasts until after the following Ramadaan.
Al-Nawawi said in al-Majmoo', 6/399:
Our companions said: It is not correct to fast on the day of doubt when it is uncertain that Ramadaan has begun, and there is no difference of scholarly opinion on this pointâ¦ But if a person fasts it to make up for a missed fast, or in fulfillment of a vow, or as an act of expiation (kafaarah), then it is permissible, because if it is permissible to observe a voluntary fast on that day for one who has a reason to do so, then it is more appropriate that one should be allowed to observe an obligatory fast. This is like the time when it is forbidden to pray (when one may nevertheless offer a prayer for which there is a reason). And if a person still owes some missed Ramadaan fasts, then he has to observe those fasts, because the time for making it up has become very short.
Reproduced from Islam QA