She fasted for six days of Shawwaal and wants to carry on fasting

Firstly:

There isnothing wrong with a person joining a voluntary fast to a made-up fast or sixdays of Shawwaal, because of the general meaning of the evidence which encouragesoffering voluntary fasts without a separation between the voluntary fast andthe made-up fast.

Secondly:

If what ismeant by your continuing to fast after completing the six days of Shawwaal isobserving voluntary fasts continually until the end of Shawwaal or for certaindays that you want to fast voluntarily, seeking thereby the pleasure of Allah,there is nothing wrong with that, so long as neither of you will be harmed bythat and neither of you will fail to fulfil the rights of the other.

However thebest teaching concerning that is not to fast for an entire month except themonth of Ramadan; rather the days when one fasts should be mixed with days whenone does not fast, and vice versa, as was the practice of the Prophet(blessings and peace of Allah be upon him).

It wasnarrated that ‘Aa’ishah (may Allah be pleased with her) said: TheMessenger of Allah (blessings and peace of Allah be upon him) used to fastuntil we said that he would not break the fast, and he used to refrain fromfasting until we said that he would not fast. And I never saw the Messenger ofAllah (blessings and peace of Allah be upon him) fast any month in full exceptRamadan, and I never saw him fast more than he did in Sha‘baan.

Narrated byal-Bukhaari, 1969

Shaykh IbnJibreen (may Allah have mercy on him) said: It is permissible to fastcontinually on consecutive days, then not to fast continually on otherconsecutive days. The evidence for that is the hadeeth quoted in the question,because that is voluntary and mustahabb.

End quote fromFataawa ash-Shaykh Ibn Jibreen

But if what ismeant is continuing to fast until the next year apart from the two days of Eidand the days of at-tashreeq (the three days following Eid al-Adha), this iswhat the scholars call lifetime fasting (sawm ad-dahr) and the ruling on it isthat it is makrooh according to the correct scholarly opinion.

And Allah knows best.