Does anyone here have a cap rate that an appraiser actually accepted without a fight on a small multifamily in a thin market

For one-to-four unit residential, lenders almost always order a form appraisal that weights the sales comparison approach heavily, with the income approach completed but treated as supporting rather than controlling. The appraiser reconciles both, and on a two or three family in a market like West Roxbury, where owner-occupant buyers compete with investors and comparable sales exist, the sales grid typically dominates the final opinion. That is the assumption doing the most work in your scenario: you are treating your 6.5 cap income value as a ceiling, but the appraiser's job is to estimate market value, and if the market is clearing at $790k to $845k, that clearing price is market value regardless of whether the implied cap rate makes sense to a pure income buyer.

The risk you did not mention is that this cuts against you in a specific way. If the appraisal comes in at $800k and the loan closes, you have not been protected by the income approach landing at $680k. You own the asset at a price the income math does not support, and the appraisal gave the lender confidence to fund it. The appraisal process in that scenario did not validate your underwriting, it just confirmed the market consensus that you already know is thin on a cap rate basis.

The income approach gets more weight on five-plus units, where residential comps thin out and the property is underwritten as commercial. At two or three units, even a careful appraiser with solid GRM and income analysis will often note the variance and reconcile toward sales. Confirm with the specific lender how they instruct appraisers on small multifamily in that zip, because some lenders do weight income more heavily on investment purchases. That is a question for their underwriting guidelines in writing.

What cap rate are you using to source your 6.5 figure, and is that derived from comparable income property sales in West Roxbury specifically or brought in from a broader Boston metro dataset?

For small residential income properties, specifically one-to-four units, lenders almost always order a form called the 1025 (small residential income property appraisal). That form requires the appraiser to run both the sales comparison approach and the income approach, then reconcile them into a single concluded value. So your income math does get considered. The question is how much weight it gets.

In a market like West Roxbury, where sales data is reasonably dense, most appraisers weight the sales comparison approach more heavily for one-to-four unit properties. The reasoning is that buyers in that segment behave partly like owner-occupants, so the market itself often reflects sales prices more than strict income logic. The appraiser will note the income approach result, but if comparable sales cluster in the $790k to $845k range, the concluded value will likely land in or near that band regardless of what a 6.5 cap produces.

That gap you have identified, $700k on income versus $820k+ on sales, is real and it does not resolve in your favor just because you ran the numbers correctly. It means the market is accepting compressed returns that your underwriting will not.

The thing worth knowing here: your income math is not wrong, it is just telling you something different from what the appraisal will tell the lender. The appraisal protects the lender against the loan exceeding the asset's market value. It does not protect you against buying an asset that will not cash flow.

A few questions would help me give you a more specific answer. What cap rate are you using for a target return, and what does your financing look like on an $820k purchase? The debt service number is probably where the real constraint shows up.