As a general rule, second mortgages, when available, do not have PMI. The loan you desire will depend not only on your score, but your combined loan-to-value (CLTV), and the lender's underwriting standards.
They are available, but generally still require at least 10% downpayment with 10% as the 2nd mortgage. If your plan is to use the 2nd mortgage to avoid the PMI payment there are other ways that usually make more sense because the payment on the 2nd mortgage is often really high and you are not much better off than paying the monthly PMI.
Yes, if you qualify there are 2nd mortgages available up to 90% loan to value and possibly 95% LTV depending on the bank or credit union. PMI is not associated with 2nd mortgages. If this is for a purchase money 2nd mortgage you will just need to make sure your 1st is at 80% or less in loan to value.
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