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In general you can. An FHA is an FHA whether it's a standard 203b or a 203k. It appears that either your Loan Officer doesn't know the program or doesn't offer it.
NOTE: With (2) late payments as recent as December and January, I would strongly caution you about validity of of Pre-Approval. With several late payments in the past 12 months it could cause a denial once your file reaches the Underwriter. When I have any borrower apply for a home loan and their credit shows any lates in the past 24 months, I will always run the AUS (automated underwriting system) to see what I am working with. I would ask your LO if they ran the AUS and ask for a least the results and even a copy of at findings just to make sure you can provide everything the Underwriter will require.
Let me know if you have any further questions.
Best of luck to you!
I think you will find many lenders that offer the FHA 203k program will likely have additional overlays and requirements you'll need to meet in order to be eligible for this program. Origination costs and fees are higher and in some instances not every consumer or every subject property is a good fit for this loan program.
In addition to what NC_Mtg_Loaner said:
Some lenders have a minimum credit score requirement of 660 or better for the 203K program & the rate & fees are generally higher which means your debt to income ratios will be affected.
It is also possible that your lender either doesn't offer the 203K or they're just not comfortable with it so they'll try to talk you out of it.
Good luck.