swiss transfer ticket-good for Mt Rigi, Titlis or Pilatus + Lucerne boats?

Elaine, The Swiss Transfer Ticket is valid for:

Journey to and from a Swiss border railway stations or airport to your vacation destination.
The transfer to and from your destination must be on one day and via the most direct route.

(quote from here: http://www.sbb.ch/en/leisure-holidays/holidays--short-breaks-in-switzerland/swisstravelsystem/swiss-transfer.html )
It is not designed for day trips. It also does not include mountain railways. See map of validity here: http://www.sbb.ch/content/dam/sbb/de/pdf/freizeit-ferien/ferien-kurztrips-schweiz/internationale-gaeste/sts-geltungsbereich.pdf

Whereas Basel SBB is a border railway station, Unless you are staying at the top of Rigi, Titlis or Pilatus I don't think you could claim that going there was a trip to or from your destination, and a boat ride is unlikely to be the "most direct route".

The Swiss Transfer Ticket costs CHF 141. A full price return ticket Basel to Luzern costs CHF 66.

So the answer is no, just get a return normal ticket to wherever you are going.

thank you. I have 2 children age 15, who would ride free on a transfer ticket. We are going from Basel to Luzern then to ZRH. We could overnight in Luzern or make it a long day trip. The cogwheel, gondolas are expensive. Thus, I was looking for a way to save money, esp. if children would ride free. We took the cogwheel in Wengen on a transfer ticket (but were staying in Wengen).

Do you have a suggestion for an affordable way for a family of 6 (3 adults, 2 teens, 1 19 yr old) to take a gondola, cogwheel, etc. in Luzern? I looked for a day pass, but it seems I must have a half price card. Could I get a half price card for 1 person and buy the book of 6 tickets for the price of 5, or do all adults need their own half price card? Or, could I buy a 1 day travel pass for my 15 year olds for them to travel for free if I am holding a regular ticket (and not a pass). Would they then travel for free on cogwheel, gondolas, etc.? Do I need to buy this online, or can I buy it at the station? thank you, Elaine

Elaine,
A half price ticket is for one person. You can't all travel on the same half price card. When you show your ticket on the train you have to show your half price card at the same time.
What you call the "book of 6 tickets for the price of 5" (Mehrfahrtenkarte) is a ticket you can stamp 6 times. It is legal for more than one person to use it at the same time, you just stamp it more than once, but if it is a half price Mehrfahrtenkarte, then you all need half price cards. Photo of a Mehrfahrtenkarte: https://pics.ricardostatic.ch/2_806356524_v1_Big/sonstige-tickets/sbb-mehrfahrtenkarten-be-lu-nw.jpg

I would recommend the trip up Pilatus. You get a boat or a train (cheaper) from Luzern to the back side of Pilatus, go up on a cog railway, and back down to Luzern. Details here: http://www.pilatus.ch/en/railway-cableways/silver-round-trip/
Drawing here: http://pilatus.webtuning-cdn.ch/webautor-data/223/Goldene-Rundfahrt_Internet-1_0.jpg
This will cost CHF 83.20 per adult, plus your fares Basel to Luzern and Luzern to Zürich. Yes, mountain railways are expnesive, but they have expensive overheads.

Children 6 to 16 normally travel half price. From your 16th birthday you pay adult fares.
But, you can get a one day pass for children. "When accompanied by an adult with a valid ticket, children aged 6 to 16 years can travel 2nd class for CHF 16 for the whole day.". Details here: http://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/children.html
However that card only gives a reduction on mountain railways.

thank you. So, you would recommend Pilatus over Rigi? Also, we would plan to do the Silver trip on a Sat. in July. Do I need to prebook, or can I just buy tickets that morning (in case it's fogged in and we don't go)?

FYI, with a Swiss Transfer Ticket, you can add the Half-Fare Card to the same purchase for $75 per adult, to use during your sightseeing. However, Chris has probably already pointed you toward a better solution for your trip; I won't try to second-guess all that.