Nope, we don’t. Our forms, like most of our hosting, are static - they are processed at build time, and we will ONLY save fields that are defined in that static definition (in an html file, in your deploy).
The trick for dynamic fields is to define ALL of them in that html file - we will happily accept form submissions with any number of fields, including 0, or 10,000 - but we will only SAVE the pre-specified fields. So, if you think someone might make 100 pet names, please predefine pet_1_name through pet_100_name at build time, so we can recognize and capture all of them at browse time