It's pretty hard to get more than one because every deal is on its own timeline (you didn't meet all the prospective investors on the same day, and each has its own internal timeline modulated by people being around and internal process). If you're really hot (and this is easier in later rounds where your A investor(s) can whip up interest) perhaps you'll get lucky, but most deals aren't, even really good ones. In fact being "hot" in your A round might be a negative predictor (I don't know) just as most child prodigies flame out. FWIW, most of my financing have been multi-TS deals and none of them have been round A.
Also when someone issues a TS (see below) you can try to run around and use it to speed someone else up. That's hard, because the person who gave it to you will pressure you to sign immediately lest the deal explode.
However you do have useful negotiating strengths even when you have only one TS. It's hard to issue one: every firm is unique but often you have to get all or most of your partners to agree; typically you only do one or two companies a year and the firm as a whole few, so nobody wants to write a TS and then not get the deal: they persuaded their partners that this is the one!. So you can push back on egregious terms, and propose alternatives to things you'd prefer were too different. If you push too much they can walk away (and then the partner will tell their partners "wow, we dodged a bullet; that CEO would have been an asshole to deal with". But don't let it get to that point.
Another way that I've done for my last two projects was write the terms ourselves and issue our own term sheet. You're already implicitly doing this as you discuss what you're looking for before getting terms from an investor so why not simply propose a deal up front? Later stages are practically that way already as the earlier rounds will have constrained various things. This works if your team already have track records of investors making money.