Hey Gabe,
Great topic, and those competitors with EMDs outranking one are seriously aggravating. You've done a really good job of brainstorming the pros and cons. Pretty much 100% of the time, I advocate for a single site approach. The potential for brand building, authority building, ease of management and protection from the ever-changing whims of Google's filters make this the smart choice. Some things to ask the client, which I'm going to pretend is called R&B Realty:
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Won't it be easier for you to build awareness of R&B serving all realty needs, than to expect consumers to somehow remember that they should go to rbfarmrealestate.com or rbhomesforsale.com? Don't you just want them to think of RBrealty.com for all of their needs?
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Is there anything about the present domain that is ruling out building awesome farm-related content? For example is the domain something like homesforsalechicago.com right now? If so, could it be that you do need to purchase a new domain, but that it needs to be a branded domain that can encompass all present and future services? Imagine if in future R&B wants to expand to commercial real estate or luxury real estate. Would they then need 4 domains? That's a rabbit hole you don't want to go down.
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Are you ready to invest? Provided that the current domain isn't making it somehow impossible to believe one could buy farm real estate from the company, I would present the company with a plan for creating the best possible section on the website for farm real estate. I would consistently publish best-in-class articles on this topic until I'd convinced Google that farm real estate is part-and-parcel of my brand, just as much as residential real estate is. I would be sure this content was highlighted from the homepage onward, and was built with good UX and good CTAs in mind. I'd invest a great deal in this, and make my pages rank highly for core terms. I'd also consider offsite marketing initiatives (both online and off) that would begin to build awareness of my brand's association with farm properties. I see far more opportunities than limits with this approach, and with the right plan, you should have no problem creating a sterling strategy for the client.
Hope these thoughts are helpful!