If by iterative HMM searching you mean updating the initial HMM on the fly after each round of search, I don't think such a tool exists that would work with HMMer-style models.

However, it would be easy to create it by simple scripting. Start with your HMM of interest and search the database with hmmsearch. Next step is to align all significant hits with the original HMM using hmmalign. Lastly, use hmmbuild to create a new HMM, and repeat all the steps.

hhblits from the HH-suite package can do all of this but with HMMs in its own format, or from a sequence alignment.

https://github.com/soedinglab/hh-suite