I inherited an interesting Curloo Tri bike, I believe built in the late 90’s. It has a Shimano 105 group set but the cassette is only a close ratio 9 speed. Can I upgrade to a 10 or 11 speed cassette or do I need to consider a new modern group set? The chainrings are 54/39. Thx
You can't just drop in a 10/11 speed cassette; 10 and 11 speed road sprockets are spaced differently than their 9 speed counterparts; a 9 speed shifter will not move the chain the right amount for use with a 10 speed cassette without additional hacks (restricting chainstops, an adapter pulley).
I'd suggest just getting a new 9 speed cassette with more favorable gear spacing. If the chainring sizes bother you, you could also put on a new crankset.
If you choose to go to 10 speed or 11 speed, you will need at a minimum a new shifter; 11 speed will need a new derailleur as well. And the shifter is probably the most expensive part to buy; buying the entire groupset might be a better deal (though questionable on value for a 20 year old bike). On top of that, 11 speed road hubs are wider than 8/9/10 speed road hubs, so you're likely going to buy another wheel if you do a 11 speed.
Depending on the rear derailleur, your cassette options may not go much beyond 27 or 28 teeth on the largest cog. Few if any older Shimano road groupsets could do anything beyond 27 officially (but in reality they have no problems with 28s).
If you're worried about the gear ratio, get a compact crankset. Tour de France-level racers don't need more than a 53, and you're not that strong. You should be able to get a higher-end 9 or 10-speed Shimano compact crankset for about $100 or so, less if you're willing to get a used one. If you go for something like an FC-R400, you can probably find one for $50 or so.
All indexing is happening in the shifters and not in the derailleur. So moving to 10 or 11 speed does not require a new derailleur. However, the pull (ratio) exercised by a 10-speed shifter is not always the same as for a 9-speed shifter. See Bicycle Rear Derailleur Compatibility for a discussion of compatibility.
My takeaway is that you should be able to move to a 10-speed without updating components.