The main rule is that contracts must be awarded in accordance with the rules set out in the bid call document (including the public agency's internal policies and procedures). A public agency may insert a broad range of reservations in a bid call document, including the right not to award a contract in accordance with the published evaluation criteria, but such reservations will not be supported by the courts if they are deemed to constitute an abuse of process (in the sense of defeating the principle of procedural fairness).
Public entities are generally free to establish the terms by which they will evaluate bids. In a tender process, public entities typically evaluate bidders based on the lowest-priced bid. In an RFP, public entities generally evaluate bidders based on, inter alia, the best value, which gives them more flexibility to take into account other factors besides just the price of the bid.
Whether or not there are any limitations regarding the offered bid price will depend on the terms outlined in the bid call document.
An alternative bid may be defined either as the submission by a bidder of a second bid which is responsive to the evaluation criteria set out in the bid call document, or as the submission of a second bid which is non-responsive to the requirements of the bid call document. The former is acceptable but the latter constitutes a non-compliant bid and will not be considered. While public agencies have a great deal of latitude in defining the requirements of their bid call documents, all bids must be evaluated equally against the evaluation criteria set out in the bid call document.