Bridge & other card games/Is there a published "Rule"
Is there a recognized and/or published rule stating that the opening bidder when bidding 3 of a suit (intended to be a preempt)determines a rebid is desirable, can he do so?
The general consensus is no, he cannot bid again. Expert Richard Pavlicek states as a universal rule
A player who makes a preemptive bid surrenders the captaincy. Only his partner may continue bidding for his side. In other words: Once you preempt do not bid again unless you are forced to do so by your partner.
Eddie Kantar advises as number 41 of his 57 bridge bidding tips.
41. After you preempt, partner is in charge and takes ALL sacrifices. Reread this one.
This is the overwhelming consensus. You have described your hand within narrow limits. Bidding again would be telling the same story twice. Partner knows what you have and can act accordingly. You have no idea what partner has so you would be acting unilaterally.