Learn Turkish: Doktor eczaneden reçetemi almamı ve dozu değiştirmememi istedi. - The doctor wanted me to get my prescription from the pharmacy and not to change the dose.

This is how Turkish forms indirect requests with verbs like istemek (to want). You take the verb almak (to get) and drop the -k to make the short verbal noun alma. Then you add the possessive ending for 'my' (-m) because the doctor wants your action. Finally, you add the accusative case (-ı) making it almamı, because this entire action is the direct object of the main verb istedi. Literally, it translates to 'The doctor wanted my getting.'

Why does değiştirmememi have me repeated twice in a row?

The first -me is the negative suffix (not to change), and the second -me is the short verbal noun suffix. After the verb stem değiştir-, you add the negative -me, then the verbal noun -me, then the possessive -m (my), and finally the accusative -i. So değiştirmememi literally means 'my not changing' as the direct object of what the doctor wanted.

Both reçetemi and dozu have the accusative case. Are they the direct objects of istedi?