How to say 'Can I continue studying Japanese?'

Question

How would I say the following:

Can I continue studying Japanese?

I was thinking something along the lines of

Watashi wa nihongo o narau no tsudukimasuka?

It's probably wrong, and I could use some help.

Answer 1

There are three issues here.

1. Transitivity

   tuduku (→ tudukimasu) is intransitive ("to continue [of its own accord]"). You need its transitive sibling tudukeru "to continue [sth.]" (→ tudukemasu).

2. Translation of "Can/May I..."

   "Can/May I [verb]?" is usually translated using ～てもいいですか -te mo ii desu ka, here tudukete mo ii desu ka.

3. Grammar

   nihongo wo narau no is a noun phrase, which should become the object of tudukeru. To make this grammatical you would need another particle wo, giving nihongo wo narau no wo tudukeru. A way to avoid two wos in the same sentence would be to substitute narau no by benkyō, for example. nihongo no benkyō wo tudukeru.

Putting everything together, I would suggest

nihongo no benkyō wo tudukete mo ii desu ka

as an improved version of your sentence.

You haven't given any context, so we can't determine whether this is a natural way of phrasing this question in your context.