Once signed, both parties are putting in good faith to make the deal close baring some crazy issues. You can definitely stay focused on putting the rest of round together, but you really shouldn’t shop around to swap out that term sheet for another lead with better terms after you already signed. (Technically it’s non-binding but would probably look quite bad). Try and get as much negotiation (and other term sheets) before you sign where you have most leverage.
Before you sign the term sheet, of course, try to get mutliple term sheets, so you negotiate for the best deal. But once it is signed, it is assumed you both are put in good faith and A LOT OF EFFORT to close the deal/aka legal due diligence etc. At least in Silicon Valley, it is rare for reputable VC firms to withdraw once term sheet is signed except for big red flags disocvered during the final due diligence (like you lied on your pitch deck, or they discover criminal fraud background). Although no shopping clause should be worded in a way to allow you to continue to talk to firms that “follow” rather than lead.