All lenders are different in what they will approve and how much they will approve you for, but it is important note that almost all of them consider debt to income (DTI) ratios as well as payment to income (PTI) ratios.
For instance, if you make $2,000 a month they will not approve you for $1,200 a month payments. Usually the maximum PTI is in the 15-20% range and overall DTI is in the 40-50% of gross income range.
I don't know what the reasoning behind the $16,000 approval was, but my guess is one of these factors played a role. If they did, then it is less likely that another lender will approve you for much more. If these were not factors, then you might be able to get approved for more somewhere else.
Hope this helps,
Justin
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