Ask which pointer should move
When a mouse is used with two computers on one desk, the useful question is not simply whether both appear in a pairing list. It is which screen should respond right now and how you will return to the other one. Start with that ordinary transition. A portable mouse can reduce the number of objects carried, but the switching routine still needs to make sense at each destination.
What the official references support
The MX Anywhere 3S product page describes Bluetooth use with up to three devices and says the compatible Logi Bolt receiver is not included. Logitech's Easy-Switch overview includes MX Anywhere 3S among supported mice and describes changing devices with a button. Together, these support a multi-device selection workflow. They do not establish that the mouse broadcasts the same input to several computers or that every receiver bearing the brand will work.
Keep the connection plan small
For each computer, note whether the planned connection is its supported Bluetooth arrangement or a compatible receiver setup. Record which device is meant to respond after switching. If one computer belongs to an organisation, check its permitted connection method before purchasing extra hardware. A mouse feature cannot resolve a managed-computer policy. Someone with a single personal laptop may not need another receiver or another pairing merely to use the mouse in a different room.
At a temporary workspace, first decide whether the visit warrants a saved pairing. A permanent extra slot can create confusion later if the machine is borrowed or rarely used. Keep the selection map meaningful rather than treating three-device capacity as a target to fill.
Do not let a familiar guide override the model
Model names differing by a letter deserve a careful read. During research, an official page headed MX Anywhere 3S contained body instructions referring to MX Anywhere 3, Unifying and an included receiver. Those details conflict with the current 3S product page. We therefore do not use that guide to certify the 3S package or receiver compatibility. A recognisable heading alone is not enough when the instructions underneath describe another configuration.
Who benefits from the extra preparation
Someone regularly alternating between compatible computers can benefit from a stable destination map. Someone expecting automatic movement across screens needs to investigate that separate software workflow rather than treating pairing capacity as the answer. Before an important session, make a harmless pointer check on the intended screen and confirm the return route. Choose the mouse for the work you repeat, with the exact connection requirements resolved, rather than for a device count in isolation.
Sources & further reading
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