objection to admissibility and jurisdiction

No, rejoinder/replica is filed when opposite party raised new plea/case in written statement.In your case opposite party has not yet filed his  written statement however you can reply the objections.

Do not be hurry to state anything unless the defendants commit through a reply to notice or file a written statement.  Till the issues are framed, you can file such amendments/rejoinders. 

Concept of Intervenor

A party in a litigation that:

• Does not have a direct interest in the lawsuit.

• Has a clearly determinable interest in the outcome of the action.

• Has been granted standing by a court for all or part of the litigation.

A party must make a timely motion to intervene, stating the grounds for intervention. The party seeking to intervene must also attach a pleading that sets out the claim or defense for which the party seeks intervention.

Accordingly the intervener, if allowed by the Court, has to be a silent spectator and can neither file written statement nor objection.

A party may intervene either:

• As of right.

• With permission of the court.

A party may intervene as of right when the intervenor either:

• Is given an unconditional right to intervene by statute.

• Has such a substantial interest in the property or transaction at issue in the lawsuit that proceeding with the lawsuit without the intervenor will impair its ability to protect this interest (unless an existing party to the lawsuit can adequately do so).

A party may intervene with the permission of the court when the intervenor either:

• Is given a conditional right to intervene by a statute.

• Has a claim or defense that shares with the main action a common question of law or fact.

In addition, governmental  may intervene with the permission of the court when the claims or defenses in the suit are based on a statute or an executive order, or any regulation, order, requirement, or agreement issued or made under a statute or an executive order.