Two methods, and the discipline for selecting comparables is the one you already own from public-company work. What changes is what the resulting multiple is a multiple of, and what level of value it produces.
The guideline public company method applies multiples from listed peers to the subject's normalised metric. It produces a marketable minority value, because a listed share price is what a passive investor pays for a small, freely tradable slice. That single fact decides which adjustments may be applied afterwards, and getting it wrong is the origin of most double-counting.
The guideline transaction method applies multiples from completed acquisitions of similar private companies. It produces a control value, because the prices in those transactions were paid for control, and it frequently embeds an illiquidity discount too, since the targets were themselves private. Applying a control premium on top of a guideline-transaction multiple charges for control twice.
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What changes when the subject is a private company?
Three things change when the subject is private, and all three usually push the multiple down.
Size is the first and largest. Listed peers are typically an order of magnitude bigger, with a broader customer base, deeper management and cheaper capital. The size premium in the build-up rate and the fundamental discount to a peer multiple are two expressions of the same fact, and applying both to the same valuation is double-counting.
Comparability is the second. A listed precision-engineering group with eleven plants across three countries and a listed customer base is not, in any useful sense, a comparable of a single-plant business with one customer at 28% of revenue. The multiple is adjusted for that, and the size of the adjustment is a judgment that must be written down.
Accounting basis is the third, and the section on normalising earnings has already made the case. A multiple derived from peers who capitalise tooling must be applied to a subject metric computed the same way.
How should the fundamental discount be presented?
The practical form of these three is a fundamental discount to the peer multiple, and the honest way to present it is as a named list with a size against each item rather than as one round percentage. A 45% discount that decomposes into size, customer concentration, growth differential and liquidity survives a challenge; a 45% discount that is simply asserted does not.
Write it down as a list with a size against each line, and the argument becomes checkable.