How extra strong does your hand have to be to do this?
As an example, the is turned down and I have:
and I'm in Seat 1. Call it?
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When you don't completely block reverse next, crossing the river with 3 trump + an off ace is a must call, So yes call it. The fact that you only block 1 out of the 3 remaining suits makes it even more imperative that you call this.
Also, your question "How extra strong does your hand have to be to do this" betrays a fundamental misunderstanding of how you should approach this spot. To get more specific you are taking Hoyle concepts to an inappropriate religious degree. All 5 of you cards matter, not just the calling portion. Hoyle is but one factor in your decision making.
Remember Seat 1, 2nd round is the most important spot in the game. You are the gatekeeper. You get to decide which loners get through and which don't. It is your responsibility to play strong defense and protect your team from those loners, 2 point calls, and to a lesser extent even 1 point calls. That's the whole idea behind calling next. You call next thinner than you would like when you don't block reverse next. And sometimes you gotta call reverse next thinner than you like when you don't block much else. This is what I mean by all 5 cards matter.
Yes we would all love to go with Hoyle every time or only go against Hoyle when we have a very strong hand, but euchre isn't that simple. It's a race to 10, we don't get to chose our cards, they chose us, and you can't pass to victory (generally speaking), and passing from seat 1, 2nd round when you don't block much will usually lead to a certain and often quick death unless Seat 2 plays like my grandma.
Some controversial hand examples of how I play seat 1, 2nd round, assume score is 0-0:
Dealer turns down a
I call next with
I'm never passing in this spot when I block nothing. Never. No trump and two off aces is good enough to go for it. I nearly have 2 tricks and I'm calling to hit my partner's range.
Dealer turns down a
I'm crossing the river in clubs. Again, with a hand that blocks nothing and has no aces, there's no way I'm handing the ball off to Seat 2. I can't do that to my team. So I call clubs, lead a club and hope for the best. Do I wanna make this call? No. Did I wanna get dealt this hand? No. But the die has been cast, and now I GOTTA make this call.