The new mortgage loan requirements vary with conventional and FHA loans. And your credit scores!!
For 3-4 family homes, the downpayment is a minimum 20%. Typically, the rent from the 2 or 3 units not occupied by you will be used to qualify for the requested loan amount.
As you stated, the lease income required from the other units in the subject property must therfore be higher than the current lease amounts for you to qualify for the mortgage loan amount that you have applied for.
The appaiser your bank is using must also validate these increased lease amounts with comparable rents in the area. A rent 4-5 times the market rate will never be verified by an appraiser.
The bank underwriter also has the authority to over-ride the appraiser when leases cannot be properly justified.
Based on your question my opinion is that this deal is going to be difficult to conclude according to the bank's requirements.
For you to close on this property, a larger downpayment will be required using the current leases. If you do not have or do not want to put more money into this property, the bank will deny your loan. Upon denial, your downpayment and application fees are refundable.
Your income is only used as a factor when evaluating your consumer debt. The reason is simple for these new underwriting requirements... many multi-family homes are in foreclosure. They were puchased with lier loans and now the real buyers are suffering the consquences. You can verify this answer with an in-depth conversation with your loan representative and underwriter.
Hope this helps.
If you are talking about buying someone out of a lease, the amount would be whatever is negotiated between both of you. The lease will always supercede the sale, so it might be more frugal to take another apartment and wait until the lease is up on the one you want and don't renew it.