Is there a 300B type amp out there with some WATTS behind it?

Here are two possible options. This is a good 300b push pull amp that puts out 22 watts (Audio Space Reference 3.1 300b Integrated Amplifier on US Audio Mart):

And this 300b SET amp is supposed to be more robust than some others:

https://www.coincidentspeaker.com/mpsip_amps.html

Frankenstein 300b mono amps

Amps build around a higher powered 300B-XLS tube, or the 520B (which is another higher powered 300B type tube) will get you around 24Watts or so. My amp which is Art Audio Jota 300B SET is an example of that design. It worked spectacularly well with speakers such as Tannoy Definition (89db) and now Fyne Audio F703 (94db) while providing the SET magical pure class A amplification.

 I understand one way to tackle the issue of using SET amps is with high sensitivity speakers.  Is there a 300B or something that gives you that same sound out there with power so you have more speaker options?

@audiovicker You have put your finger on the classic issue with tube power. Its expensive and difficult to get right. If you look back to the 1950s before the transistor, you'll see that high efficiency speakers like Altec, JBL, Klipsch and EV were common.

If you really want to hear what your amp is about, in most rooms speakers with efficiency north of 100dB is what you need. My speakers are 98dB but running a 300b amplifier on them will not show off what the 300b does. You really do need that kind of efficiency! This is because if you really want to know what the amp does, it should never be asked to make more than about 20-25% of its rated power! Otherwise distortion colors its presentation too much.

If that's not an option you'll need more power. That likely means a push pull amplifier, since 8 Watts or so is really the upper power limit of SETs where they can be considered 'hifi' in terms of bandwidth. SET's single biggest Achilles Heel is bandwidth and power- above 8 Watts bandwidth suffers so much that if you have a speaker that is truly full range, you'll notice that there's a problem!

If you have three way speakers that can be biamped you can use a 300B SET on the midrange and tweeters and a SS amp on the bass.Then you get the best of both worlds.Supratek make preamps [duals] that even have two different tubes-one for driving bass and the other mid and tweeters so you can further optimize that configuration.

Late to the party, but there is a unique and rare Cary Audio 300b amp that outputs 20wpc using KR300b XLS. 300b SEI LX-20. It has higher fixed bias, more powerful output transformers and circuit that puts 550V on the grid. Downside is the KR tubes are $1,300/pr.  I also have a Willsenton R800i 845, with 300b driving 845 output tube to 23 wpc.  
 

I can’t get either amp to one-half on the volume pot with 99dB sensitive Klipsch Fortes.  They also drive my Focal Aria quite well at 91 dB. The Cary has a taller, deeper soundstage, but not by much.  The mids and treble are about the same, the Willsenton has a touch more bass, but both have SET sweetness.  The Cary is a zero feedback design, the Willsenton is a feedback design, but the Cary distorts less at higher volume du to stability of the KR tubes.

If I had to pick one, I’d pick the Cary. I’m fortunate enough to keep both, each in a different room with different rigs.