You do not indicate that this is a task order under an IDIQ contract which allows for both cost-plus-incentive-fee (CPIF) and firm-fixed-price (FFP) CLINs, so I will assume that is not the case. Also, your question implies the current contract structure is CPIF with added performance incentives, since a CPIF construct alone would only compare final cost to target cost to determine fee earned (incentivizing only cost control) and would not include a "performance plan" as you describe. Regardless of the current contract construct, I can see several potential issues with an attempt to convert from one contract type to another contract type not contemplated in the original contract, as discussed below.
If you attempt to issue the change unilaterally, the contractor could object the change is not permitted under the Changes clause at FAR 52.243-2. To be permissible, the clause requires the change to be (1) "within the general scope of this contract" and (2) a change in drawings/designs/specifications (if supplies are to be specially manufacturing in accordance with such documents), or method of shipment or packing, or place of delivery. Per the Supreme Court in Freund v. United States (260 U.S. 60 (1922)), a change is within scope if it "should be regarded as having been fairly and reasonably within the contemplation of the parties when the contract was entered into." In the years since the courts have interpreted this ruling in various ways, with varying degrees of liberality, but in general courts look to whether the change creates a bargain that is materially different from the parties' original bargain. FFP contracts typically have a higher prices than cost-reimbursement contracts, reflecting the greater risk assumed by the contractor. Changing contract type from CPIF to FFP shifts more risk to the contractor. (If not, you would not be trying to make this this change.) The contactor may argue this shift in risk materially alters the bargain, hence is out of scope. This argument may or may not be successful; I have found no case law that specifically addresses it. Negotiating a fair FFP equitable adjustment may lessen the odds the contractor would raise such an objection.
Even, if the contractor does not argue the change is out of scope, a third party might under a protest. Only modifications that are within scope are exempt from the Competition in Contracting Act (CICA) requirements for full and open competition absent an approved J&A. (See FAR 6.001(a).) Courts will not allow an agency to use modifications to circumvent CICA. In general, courts and GAO look to whether there is a material difference between the modified and originally competed contract, such that the field of competition would have been materially different had the original solicitation reflected the contemplated changes. If so, the change is out of scope and may not be made under the contract absent an approved J&A. Cost reimbursement contracts have unique requirements such as an approved accounting system that not all commercial entities can meet. Such an entity may protest that, had the original solicitation been fixed price, it would have submitted an offer. This is just one example of an argument a potential competitor could make. Again, whether such an argument would succeed is unknown, but the agency should consider the potential for such scope arguments.
The contractor might also argue that the change is not of a type allowed by the Changes clause because it is not a change in drawings/designs/specifications, method of shipment or packing, or place of delivery. In this regard, while courts have been fairly liberal in interpreting what is encompassed by a change in "specification," it appears to be a stretch to deem a change in contract type as being a type of change allowed by the Changes clause.
In summary, there is no clear "yes" or "no" to your question, that I am aware of, since I can find no case law that directly addresses this precise situation, but you should consult your legal counsel and contracting officer for guidance before considering a unilateral, or even bilateral, change in contract type.
As an aside, some may be tempted to rely on FAR 16.103(c) as "authorization" to make the change in contract type. It says, "In the course of an acquisition program, a series of contracts, or a single long-term contract, changing circumstances may make a different contract type appropriate in later periods than that used at the outset. In particular, contracting officers should avoid protracted use of a cost-reimbursement or time-and-materials contract after experience provides a basis for firmer pricing." I do not read this as authorizing a change in contract type after award, especially unilateral change. I believe this is simply a caution to consider up front during acquisition planning the potential future need to use a different contract type, and to structure program contracts accordingly. Certainly the contractor not bound by this language since it is not embodied in a FAR clause, unless it is specifically incorporated into the contract by special clause or reference