I think it would make more sense in English to say "I put on many clothes".

English English - not translations but a variety of typical sayings... I'm getting dressed, I'm putting on extra layers, I'm dressing up. Unfortunately "I dress with many clothes" is not amongst them. Can't imagine any UK native English speaker saying this, nor for that matter any American I've ever met. What would be good to know is whether this is actually a common phrase in Romanian or something invented for this course.

The more literal translation, "I dress myself ..." is fairly common in spoken American English.