Which speakers, if any, combine the strengths of Harbeth and ProAc ?

Both very good speaker manufacturers. 
Unfortunately, your question is dependent upon the listener's ears.
For me, the answer is Vandersteen.
B

Probeth Model 3 (Anniversary Edition)

What are the strengths of each brand that you are looking for?

I've owned 3 Proac models and subsequently 3 Harbeth models over a period of about 30yrs.
I've owned ATC for the last couple of years.
While they have all been fine speakers, I've found ATC to offer superior timing, dynamics and broadband neutrality built around engaging and realistic mids.  
For me ATC are the more flexible, in the sense of sounding confident and convincing with any type or genre of music - classical/jazz/rock/electronic etc - which suits my eclectic music tastes.

Rockport and Verity Audio come to mind.

Verity and Reynaud

+1 for Vandersteen. I owned Harbeth speakers for years, various versions of the SHL5 and the model 40. I also had Proac Response 3's. For me the Vandersteen's do everything the Harbeth's and Proacs do well and build upon those strengths. My advice too you would be to go listen to any of the speakers recommended in this thread. Your opinion is the only one that counts. Good Luck!

Hard to go out and listen to these days. And I am not in a hurry, just thinking that I might want to go in this direction soon enough.
Vandersteen is very popular, and I am sure for good reasons.
ATC is interesting. Active or passive ? Which models ?
Verity and Reynaud..why not?
Rockport - too expensive.
Any of those can work equally well with both SS and tube amps ?
It is a common wisdom that Harbeth need SS and ProAc are better, generally speaking, with tubes.
ATC would need a lot of SS power, unless already powered, correct ?

@inna
" It is a common wisdom that Harbeth need SS and ProAc are better, generally speaking, with tubes." Says Who?
 

Harbeths are designed to present an ‘easy’ electrical load to the amplifier and will work well with valve (tube), solid-state and digital amplifiers. Playing loudly in a large acoustically dry, well-furnished room will demand a powerful amp. Conversely in a smaller setting listening closer to the speakers, much less power will be needed.

Verity is tube friendly. 

I'm running my SHL 5 Plus with a 55 watt per channel tubed integrated. My friend was running his 40.2s with a 48 wpc tubed integrated. Both setups work just fine.

I didn't know they had any. Harbeths are seriously over priced. Is that a strength?

inna OP6,097 posts
ATC is interesting. Active or passive ? Which models ?
ATC would need a lot of SS power, unless already powered, correct ?

I currently own 2 ATC models, the passive stand mount SCM19 and big(ish) SCM100 active towers.
The 19's require a decent amount of power, 120 -150W, and quality SS would be best IMO to exploit their superior dynamics and bass tautness. The 19's replaced my Harbeth M30.1's.
Ultimately, active is the way to go with ATC and I love my SCM100aslt's - but if you already own a suitable amp the passives are still great.
Which model depends on how much you're prepared to spend and what your room will accomodate. 
Definitely worth a listen to see if the ATC sound appeals. 

Rockport similar to either of these? Not in my experience. In fact if Harbeth dreams it has anything in common with Rockport, it would need to wake up and apologize. ProAc to a lesser degree but I simply think we are talking about speakers on an entirely different level. 

I drove my Harbeth SHL5+ 40th Anniversary very easily and quite high volumes remained beautiful with an 87 watt VAC integrated. Lovely. I recently bought a DarTZeel CTH-8550 and the additional power (200 watts stated but Stereophile measured much higher) of course controls the speakers a bit better but with other trade-offs. The SHL5+ only drops to 6 ohms and is up to 10 ohms so they are very easy to drive. I’m moving to a bigger home so I’m seriously looking at 40.2/3. The SHL5+ 40th are especially nice with the bi-wire WBT post. I emailed Harbeth and for the SHL5 and 40.2 there are no difference between the 40th Anniversary and the XD it’s just that the 40th Anniversary was in 2019 so they needed to re-name them for 2020 and beyond. The lower speakers were upgraded with the new crossover. The SHL5 actually lost the bi-wire capability and the new SHL5+ XD has only 2 speaker posts. I’m a fan. I previously had Sonus Faber.