The following was forward to me in 2018 concerning 90 day visa extension for US citizens. The person (Duncan Sweet from Mid Atlantic Yacht Services) called Horta Immigration and these were the general guidelines:
"The Portuguese Immigration office in Horta will provide a Schengen visa extension given the following documents for submission;
1) Passport well in advance of the Schengen visa expiry
2) Certificate of Registry for the yacht
3) means of sustenance = savings and/or investment account summary/extract
4)
health insurance coverage valid for EU and/or repatriation
5) short concise petition for Shengen visa extension outlining plans for cruising, visiting other islands etc
If someone wants to overwinter they should consider applying for a residency visa which has similar requirements as outlined above
My understanding is the cost of a Shengen extension is @ €100.00."
I inquired at several Immigration offices in Azorean islands and in Porto Santo (near Madeira), they all confirmed. These offices added requirement that you must apply at your
current Portuguese Immigration office and wait at that location to get a copy in writing. They (the immigration office would not forward to another location. Again this was in 2018 but hope it helps--Saltysailor