It must be accepted: I can take you something. Please fix it. Dzekuje bardzo.
Added "I can get you something", but "I can take you something" has literally four results in Google and doesn't seem to me like something a native would say...
Yes. This native wouldn't say "I can take you something". "I can bring you something" would be an alternative with the same meaning in English.
"I can take something for you" is what you say to your neighbour when he asks if you can accept a delivery (e.g. parcel) for him. "I can get you / take you something" has a very different meaning — more along the proactive robić / kupić lines — "I can make / do / buy / fetch something for you".
Which of the two meanings does "Mogę coś wziąć dla ciebie" have?
Rather not the first one, if you accept the delivery, I'd use 'odebrać', and besides, it's not 'something' then but a very specific delivery.
Well, take/get/bring something from the shop, something from my house (you don't have gloves? I have an extra pair at home, I can take them and lend it to you), things like that.