Although this won't help you in this instance because you want to book JetBlue, I have been able to do something similar from an airport's site, specifically PNS'
www.flypensacola.com. The booking engine allows multi-destination, open jaws, & any flight routings (doesn't have to be via PNS), and international as well as domestic flights.
Additionally, ITA software allows you to construct the itinerary you want (using multi-segment)
http://matrix.itasoftware.com/cvg/dispatch/prego. It will show both JetBlue & Virgin Atlantic flights, among many others, for your particular itnerary. Selecting "Choose flights (text)" at the top of the page enables you to choose particular flights, one at a time, for each portion of your trip (whether it be a one-way, round trip, or a multi-segment trip), in any order you like.
ITA is only a search engine, not a booking site, so you will have to take the results to a travel agent to book (but you have done the research). The results are from the latest CRS loaded inventory for published fares. The booking details generated by the site to present the travel agent would look something like this:
If you want to buy this ticket, it's probably best to use a travel agent (this ticket involves multiple airlines, which can get complicated). If you use a travel agent to buy this ticket:
If your travel agent is online and has an e-mail address, e-mail this itinerary to them
If your travel agent is not online, print out this page and fax/give it to them
It is very important to use exactly the same booking codes and fare codes that we've used on this page in order to match the price we've found.
Fare (A1): B6 SYRNYC K fare (rules) $147.91
Fare (B1): VS NYCLON NHXAP fare (rules) $318.00
Fare (B2): VS LONNYC NHXAP fare (rules) $318.00
Fare (A2): B6 NYCSYR L7 fare (rules) $73.49
Tax: US International Departure Tax $15.10
Tax: US International Arrival Tax $15.10
Tax: United Kingdom Passenger Service Charge £14.10
Tax: United Kingdom Air Passengers Duty £40.00
Tax: US Customs Fee $5.50
Tax: US Immigration Fee $7.00
Tax: USDA APHIS Fee $5.00
Tax: VS YQ surcharge $122.00
Tax: US September 11th Security Fee $7.50
Tax: US Passenger Facility Charge $13.50
--------------------------------------------------------------------------------
Total for 1 adult passenger: $1159.10
(as of Wednesday, July 25, 2007 11:11am)
Fare construction (sometimes useful to travel agents):
SYR B6 X/NYC 147.91K VS LON 318.00NHXAP VS X/NYC 318.00NHXAP B6 SYR 73.49L7 NUC 857.40 END ROE 1.00 FARE USD 857.00 XT 5.50YC 7.00XY 5.00XA 30.20US 7.50AY 82.40GB 29.00UB 122.00YQ 13.50XF SYR4.50 JFK4.50 JFK4.50
The ITA Software FAQ is at
http://matrix.itasoftware.com/cvg/dispatch/help/faq.
Good luck.