I agree with others that you can frame this positively. You have several possible opportunities (interviews and/or offers) and of course you want to have all the information about your choices to enable you to make your decision.
It might push them to make you the best kind of offer they can (where they have flexibility). But it doesn’t tell them anything negative - you are telling them that you are in demand, which is a good thing. Other employers will also want good candidates.
i don’t think it’s a problem that they’re somewhat diverse roles. My 3 interviews are for 3 very different roles: one public sector (with a different job title to the others, but drawing on some of the same skills), one private sector company, and one a consultancy (that serves public and private sector clients).
I’ve spoken to the latter who are keen to make an offer it seems. The diversity involved reinforces their assessment of me as having a diverse and adaptable range of skills. I’ve told them about the timescales involved (and the recruiter has worked in the public sector, so he’s aware that it won’t necessarily be a rapid process!) and that I would want to have all the information available to me so I can weigh up my options before making a decision.
The context itself may push them to making me the best offer they can. Regardless of any negotiations, I (quite reasonably) want to make sure I’m making the right decision for me and my career, based on the offers available to me.
Anyone would.
The weird situation you describe in teaching is just a reflection of the level of dysfunction in that profession generally. Elsewhere, organisations realise that people will need time to consider and decide on an offer. It’s a big decision and they need to be sure it’s the right move for them. Not just at senior levels (or mid-senior levels), but at any level really.
Where you’ve applied and are waiting to hear back about an interview or not, I wouldn’t hold out on decision making. But remember that you can change your mind about an offer at any time. Or decide to accept a different job shortly after starting. You can frame it on your CV about an outstanding opportunity coming up and you needing to change. So long as your CV isn’t covered in stints in jobs measured in days or weeks, it shouldn’t set alarm bells off.