In broad terms, if you don’t want to accept an offer of severance, then your main options are to:
But before taking those steps, it is wise to consult a lawyer so you know the terrain before commiting to a direction.
Negotiate
Often a negotiation would start with a counteroffer from you. Negotiating simply involves working with the other party towards a mutually acceptable out-of-court resolution. You can engage a lawyer to negotiate on your behalf or you can engage directly with your employer (or their legal counsel). Which of those two is best depends on the situation.
A lawyer can provide various degrees of assistance short of full-representation, if that is your preference, such as research, ghost writing correspondence, and advice about negotiation strategy. Negotiations can also be assisted by a mediator.
Litigate
If the matter doesn’t resolve early through negotiations, you may eventually have to decide if you want to sue to enforce your rights. Generally that would mean using the courts, but administrative tribunals or private arbitration may also be options. Even if you start litigation, you can still remain open to a negotiated settlement.
Wait
Odd as it may sound, in some circumstances it can be good strategy to put your claim on the back burner for a while (but not for too long – don’t forget there are limitation periods on different types of claims, and the law encourages people not to sit on their rights).
Slowing things down can have advantages in light of the duty on employees to mitigate their losses. In a case of wrongful dismissal, a plaintiff is not always straightforwardly entitled to full pay in lieu notice. There is usually an obligation on the dismissed employee to try to mitigate their losses by looking for alternative employment. Any income earned over the notice period offsets (or reduces) the damages payable. Moreover, a judge can withhold some or all of an employee’s compensation if the employee turned down reasonable alternative employment or failed to make adequate efforts to get new work.
One upshot of the duty to mitigate is that the value of an employee’s claim is somewhat uncertain until the notice period has expired. For that reason, if early negotiations have not borne fruit, some employees can gain an advantage by waiting to see what happens with their mitigation efforts and then re-engage in negotiations after the value of their claim has crystalized. Note, however, this strategy can cut both ways: if you don’t mitigate, your claim against the employer may be strong; but if you do mitigate, if may be less valuable than it appeared before negotiations were put on hold.