Short answer. No. Both are on the list of pleadings and motions the rule expressly bars in this kind of case: third-party complaints and interventions are named as prohibited, alongside several other pleadings and motions the rules do not allow in this summary proceeding.
What the law says
The following petitions, motions, or pleadings shall not be allowed: 1. Motion to dismiss the complaint except on the ground of lack of jurisdiction over the subject matter, or failure to comply with section 12; 2. Motion for a bill of particulars; 3. Motion for new trial, or for reconsideration of a judgment, or for reopening of trial; 4. Petition for relief from judgment; 5. Motion for extension of time to file pleadings, affidavits or any other paper; 6. Memoranda; 7. Petition for certiorari, mandamus, or prohibition against any interlocutory order issued by the court; 8. Motion to declare the defendant in default; 9. Dilatory motions for postponement; 10. Reply; 11. Third-party complaints; 12. Interventions
Rule 70, Section 13 — Prohibited pleadings and motions. Read the full provision →
Both are named specifically on the prohibited list
The rule lists twelve categories of petitions, motions, or pleadings that shall not be allowed, and the last two entries are exactly what you asked about: third-party complaints and interventions. There is no ambiguity here at all — these are not simply omitted from a list of what is allowed, they are affirmatively and specifically named as barred procedural tools in this type of case.
Why ejectment cases exclude these procedural tools
Ejectment is designed as a summary proceeding, meant to resolve possession quickly rather than draw in additional parties or claims that could complicate and slow it down. Third-party complaints and interventions typically expand a case to bring in new parties and new issues, which runs directly against the streamlined, tightly focused nature this particular kind of proceeding is deliberately built around from the start.
Other pleadings are barred for the same underlying reason
The prohibition is not limited to these two. The same list bars motions for a bill of particulars, motions for new trial or reconsideration, petitions for relief from judgment, motions for extension of time, memoranda, certain certiorari-type petitions against interlocutory orders, motions to declare a defendant in default, dilatory postponements, and replies. All of them share the same underlying purpose: keeping the ejectment case moving forward quickly, without the kinds of delays these procedural devices commonly introduce into an otherwise summary proceeding.
What options remain available to you instead
Since a third-party complaint or intervention is not an available route in someone else's pending ejectment case, whatever genuine interest you have in the matter would need to be pursued through whatever other avenues the rules do actually permit, rather than filing directly within the pending ejectment proceeding itself, since that specific procedural door is closed to both of these particular devices in this proceeding.