Hi @PhebeM
Yes, TurboTax can handle these kind of donations! You will find it easy to enter them on TurboTax Online or Desktop!
You can carryover your contributions that you are not able to deduct in the current tax year because they exceed your adjusted-gross-income limits. You can deduct the excess in each of the next 5 years until it is all used but not beyond that time.
You can find these limits HERE
Thank you for using TurboTax!