It depends on what you mean by 'attend'. If you only spend a minute or two at each celebration before rushing back to your private jet to race to the next location, you could conceivably 'attend' something like 60 different New Year's celebrations. If you start at the international date line and race away from the sunrise all day, you have 48 total hours of the 'day' in which to celebrate. However, you'd have a hard time finding New Year's parties across Asia that start 24 hours before midnight of the New Year.
If attendance requires you to be physically present at the exact moment that the clock strikes midnight, your number of parties are limited to the number of distinct time zones. There are 27 time zones that are whole hour offsets from Greenwich Mean Time, counted from UTC+14 to UTC-12, but it's impossible to visit unique nations in every time zone. Additionally, there are a few fractional-hour time zones such as the Chatham Islands in New Zealand (UTC+12:45), parts of Australia (UTC+10:30 and UTC+9:30), Myanmar (UTC+6:30), Nepal (UTC+5:45), India (UTC+5:30), Afghanistan and Iran (UTC+4:30), Newfoundland Canada (UTC-3:30), and Venezuela (UTC-4:30). Thus, if you can find a unique nation in each and every time zone, it is technically possible to 'attend' 35 different national New Year's celebrations. You could have five separate celebrations in the two hours between midnight UTC+7 and midnight UTC+5 alone!
Personally, I recommend this schedule: Kiritimati, Tonga, the Chatham Islands, Suva, New Caledonia, Lord Howe Island, Papua New Guinea, Manokwari, Manila, Ho Chi Minh City, Yangon, Shigatse, Kathmandu, Lucknow, Lahore, Kabul, Dubai, Basra, Jerusalem (Israel or Palestine, depending on your politics), Naples, Italy, Casablanca, Mindelo, Fortaleza, Paramaribo, Newfoundland, Bermuda, Maracaibo, Nassau, Guatemala City, Cabo San Lucas, Clipperton Island, Honolulu.
How practical is this schedule? Not very. Assuming it takes six minutes to get off the plane, go to the party, kiss someone at midnight, and get back on the plane. That leaves... three hours 20 minutes of party time and 19 hours 40 minutes of travel time.
You'd have to travel on average thousands of miles per hour, peaking at Mach 26 between the Chatham Islands and Fiji. With those G-forces, there'd probably be some medical consequences that you can't just walk off. You might even die. Also, you have to have flight clearance over dozens of nations, some of which have a rather "shoot first and ask questions later" approach to mysterious aircraft entering their hairspace unannounced.
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