Can I book groups on SATA involving flights on TAP or other airlines (WestJet / Alaska Airlines / Air France / Binter)?

Yes. However, the offered price for the flight operated by another airline is a base price. When an airline evaluates a group, it may offer a higher value. This will only be confirmed by the respective airline after the booking has been made. 

If there is already a confirmed group booking on SATA flights, and it is intended to change to a flight not operated by SATA, it implies that after accepting a new price, the confirmed SATA flight is automatically canceled and the flight operated by the other airline is awaiting confirmation by the new operating airline.

Why does the SATA website show fares lower than the ones offered to the group?

SATA offers promotional fares on several routes to its individual passengers. These are reduced value fares, which exist in a limited number of seats and, as such, imply advance payment, do not allow change names, do not allow date changes, and are subject to seat availability on the same class of service (so that a fare difference would not be needed), plus change penalties.

How can I request a group quote?

IATA Travel Agent: After logging in to SATA4AGENTS, a GROUPS tab will be available in the main menu. By clicking on this tab, you will have immediate access to the Group Quote Request form.
Non-IATA Travel Agent: After logging in to SATA4AGENTS, a GROUPS tab will be available in the main menu. By clicking on this tab, you will have immediate access to the Group Quote Request form. Pay attention to the GDS fields: and Office ID / PCC: which must be filled in Amadeus in the GDS field and PDLS40128 in the office ID/PCC field.