After you receive (S) Chain 4 (and later (S) Chain 16), you are able to chain several battles together. Upon activating a scan, multiple Noise can be tapped in addition to the first selected (a total of four Noise with (S) Chain 4 and sixteen with (S) Chain 16). Each battle will be fought in succession, with no breaks or chance for recovery in between. Status will also be carried over from battle to battle, including your current HP, Pin Limit and Reboot levels, the number of remaining charges on limited-use Pins, and Fusion level (as well as the number of stars currently filled).
Your drop rate will be multiplied by the number of battles you will be fighting, and the Amount of PP Obtained will increase depending on the amount of reductions. However, the Noise increase in difficulty after each additional round. If you lose and select Retry, you will restart on the first battle in the chain. It is also prudent to mention that as part of the methods of gaining the secret reports, you must not chain the Boss Noise symbols with anything else (including Taboo Noise, and other Boss Noise) or it will not count.
Official Sticker Descriptions:
(S) Chain 4: Lets you chain up to 4 battles at once. Enemies grow stronger with each "reduction" (round), but also drop pins more often.
(S) Chain 16: Lets you chain up to 16 battles at once. Enemies grow stronger with each "reduction" (round), but also drop pins more often.
Tips: Touch multiple Noise symbols to chain battles! But beware: chaining makes enemies tougher. Sometimes it's wise to stick to a single round.