Alternative jurisdiction answer: england-and-wales
These sort of tactics don't work. The Courts have a number of tools available to them to prevent it under the Civil Procedure Rules.
Overriding objective
First, CPR 1.2 - 1.4 require the Court and the parties to give effect to the court's overriding objective:
1.2 The court must seek to give effect to the overriding objective when it
– (a) exercises any power given to it by the Rules; [...]
1.3 The parties are required to help the court to further the overriding objective.
1.4 (1) The court must further the overriding objective by actively managing cases.
1.4 (2) Active case management includes – (a) encouraging the parties to
co-operate with each other in the conduct of the proceedings; [...];
(c) deciding promptly which issues need full investigation and trial
and accordingly disposing summarily of the others; [...]; (h)
considering whether the likely benefits of taking a particular step
justify the cost of taking it; (i) dealing with as many aspects of the
case as it can on the same occasion; [...]; (l) giving directions to
ensure that the trial of a case proceeds quickly and efficiently.
The overriding objective is found at CPR 1.1:
(1) These Rules are a procedural code with the overriding objective of
enabling the court to deal with cases justly and at proportionate
cost.
(2) Dealing with a case justly and at proportionate cost includes, so
far as is practicable – (a) ensuring that the parties are on an equal
footing and can participate fully in proceedings [...]; (b) saving
expense; (c) dealing with the case in ways which are proportionate –
(i) to the amount of money involved; (ii) to the importance of the
case; (iii) to the complexity of the issues; and (iv) to the financial
position of each party; (d) ensuring that it is dealt with
expeditiously and fairly; (e) allotting to it an appropriate share of
the court’s resources, while taking into account the need to allot
resources to other cases; [..]
This means that the Court is going to have very little patience for a party which deliberately tries to overwhelm the other party with interim applications (what the US refers to as "motions").
Case management powers
The Court can use its case management powers under CPR 3.1:
(2) Except where these Rules provide otherwise, the court may – [...]
(k) exclude an issue from consideration; [...] (m) take any other step
or make any other order for the purpose of managing the case and
furthering the overriding objective [...]
Or it can strike out a statement of case under CPR 3.4:
(2) The court may strike out a statement of case if it appears to the
court – (a) that the statement of case discloses no reasonable grounds
for bringing or defending the claim; (b) that the statement of case is
an abuse of the court’s process or is otherwise likely to obstruct the
just disposal of the proceedings;
Cost implications
The Court has discretion as to what (if any) costs order to make. Under CPR 44.2(2):
(2) If the court decides to make an order about costs – (a) the
general rule is that the unsuccessful party will be ordered to pay the
costs of the successful party; but (b) the court may make a different
order.
CPR 44.2(4) provides:
In deciding what order (if any) to make about costs, the court will
have regard to all the circumstances, including – (a) the conduct of
all the parties;
And CPR 44.2(5) provides:
The conduct of the parties includes – [...] (b) whether it was
reasonable for a party to raise, pursue or contest a particular
allegation or issue; (c) the manner in which a party has pursued or
defended its case or a particular allegation or issue;
Those rules cover what costs order the Court makes (e.g. it could decide to depart from the general rule by not awarding the winner costs, or even by awarding costs to the loser). But the Court also has discretion as to how much those costs should be. CPR 44.4 provides:
Factors to be taken into account in deciding the amount of costs
44.4 (1) The court will have regard to all the circumstances in deciding whether costs were – (a) if it is assessing costs on the
standard basis – (i) proportionately and reasonably incurred; or (ii)
proportionate and reasonable in amount, or (b) if it is assessing
costs on the indemnity basis – (i) unreasonably incurred; or (ii)
unreasonable in amount.
(3) The court will also have regard to – (a) the conduct of all the
parties [...]
Civil restraint orders
Ultimately, for the most extreme cases, the Court could issue a civil restraint order under CPR PD 3C. This would prevent a party from making further applications and/or any claims (depending on the type of restraint order) without the Court's permission.
Under CPR 23.12 the Court must consider doing this every time it dismisses an application which is without merit:
If the court dismisses an application (including an application for
permission to appeal or for permission to apply for judicial review)
and it considers that the application is totally without merit – [...]
(b) the court must at the same time consider whether it is appropriate
to make a civil restraint order.