What attachments should every BSC have in its arsenal (and what would they be used for)? 

A floor tool that transitions from carpeting to hard flooring is a must to eliminate time loss from switching tools. An upholstery tool and a dust brush address detail cleaning on furniture, blinds and architectural details. A crevice tool is one of the most essential tools for hard to reach areas. Crevice tools vary in length between 11 and 28 inches and can clean in tight places where you might otherwise need to move furniture or appliances to reach, which can be a huge time saver.
— Rich Steinberg, Vice President of Sales, ProTeam, Boise, Idaho

It really depends on the requirements of the job, if the contract includes ducts and vents to be cleaned than a high level kit or extension tubes should be on site. Are they required to vacuum the drapes or blinds, what about chairs and upholstery? Again, it all depends on the specs of the job, it doesn't mean the cleaner has to carry these items with them however there may be times when these tasks are done as project work.
— Gareth Mason, President, NaceCare Solutions, Mississauga, Ontario, Canada

Dust brush, crevice tool, bare-floor tool, carpet tool to be used in detail cleaning of hard to reach areas.
— John McDonnell, Marketing Manager - Commercial and Dealer Division, Hoover, Glenwillow, Ohio

There are several attachments that all BSC’s should have, particularly for above floor cleaning. The first is an upholstery tool for cleaning upholstery, pillows, car interiors and stairs. A second attachment is a crevice tool for those hard to reach places. Finally, I recommend a dusting brush for dusting furniture, baseboards, lamps and lampshades.
— Dalvin Green, Product Manager - Commercial Brands, Electrolux Home Care Products North America, Charlotte, N.

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