diff --git a/test/algorithms/Chalmet.jl b/test/algorithms/Chalmet.jl
index 16e85a8..5221b24 100644
--- a/test/algorithms/Chalmet.jl
+++ b/test/algorithms/Chalmet.jl
@@ -206,6 +206,23 @@ function test_vector_of_variables_objective()
     return
 end
 
+function test_too_many_objectives()
+    P = Float64[1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 1 0]
+    model = MOA.Optimizer(HiGHS.Optimizer)
+    MOI.set(model, MOA.Algorithm(), MOA.Chalmet())
+    x = MOI.add_variables(model, 4)
+    MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
+    MOI.add_constraint.(model, x, MOI.LessThan(1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
+    f = MOI.Utilities.operate(vcat, Float64, P * x...)
+    MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
+    @test_throws(
+        ErrorException("Chalmet requires exactly two objectives"),
+        MOI.optimize!(model),
+    )
+    return
+end
+
 end
 
 TestChalmet.run_tests()
diff --git a/test/algorithms/EpsilonConstraint.jl b/test/algorithms/EpsilonConstraint.jl
index 1607760..e24aa58 100644
--- a/test/algorithms/EpsilonConstraint.jl
+++ b/test/algorithms/EpsilonConstraint.jl
@@ -467,6 +467,23 @@ function test_vector_of_variables_objective()
     return
 end
 
+function test_too_many_objectives()
+    P = Float64[1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 1 0]
+    model = MOA.Optimizer(HiGHS.Optimizer)
+    MOI.set(model, MOA.Algorithm(), MOA.EpsilonConstraint())
+    x = MOI.add_variables(model, 4)
+    MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
+    MOI.add_constraint.(model, x, MOI.LessThan(1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
+    f = MOI.Utilities.operate(vcat, Float64, P * x...)
+    MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
+    @test_throws(
+        ErrorException("EpsilonConstraint requires exactly two objectives"),
+        MOI.optimize!(model),
+    )
+    return
+end
+
 end
 
 TestEpsilonConstraint.run_tests()
diff --git a/test/algorithms/Hierarchical.jl b/test/algorithms/Hierarchical.jl
index 0f10785..c6d1279 100644
--- a/test/algorithms/Hierarchical.jl
+++ b/test/algorithms/Hierarchical.jl
@@ -36,8 +36,11 @@ function test_knapsack()
     P = Float64[1 0 0 0; 0 1 1 0; 0 0 1 1; 0 1 0 0]
     model = MOA.Optimizer(HiGHS.Optimizer)
     MOI.set(model, MOA.Algorithm(), MOA.Hierarchical())
+    @test MOI.supports(model, MOA.ObjectivePriority(1))
     MOI.set.(model, MOA.ObjectivePriority.(1:4), [2, 1, 1, 0])
+    @test MOI.supports(model, MOA.ObjectiveWeight(1))
     MOI.set.(model, MOA.ObjectiveWeight.(1:4), [1, 0.5, 0.5, 1])
+    @test MOI.supports(model, MOA.ObjectiveRelativeTolerance(1))
     MOI.set(model, MOA.ObjectiveRelativeTolerance(1), 0.1)
     MOI.set(model, MOI.Silent(), true)
     x = MOI.add_variables(model, 4)
diff --git a/test/algorithms/Lexicographic.jl b/test/algorithms/Lexicographic.jl
index a255b85..a9f8ed3 100644
--- a/test/algorithms/Lexicographic.jl
+++ b/test/algorithms/Lexicographic.jl
@@ -27,6 +27,7 @@ function test_knapsack()
     model = MOA.Optimizer(HiGHS.Optimizer)
     MOI.set(model, MOA.Algorithm(), MOA.Lexicographic())
     @test MOI.supports(model, MOA.LexicographicAllPermutations())
+    @test MOI.supports(model, MOA.ObjectiveRelativeTolerance(1))
     MOI.set(model, MOA.LexicographicAllPermutations(), false)
     MOI.set(model, MOA.ObjectiveRelativeTolerance(1), 0.1)
     MOI.set(model, MOI.Silent(), true)
@@ -175,6 +176,27 @@ function test_warn_all_permutations()
     return
 end
 
+function test_knapsack_time_limit()
+    P = Float64[1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 1 0]
+    model = MOA.Optimizer(HiGHS.Optimizer)
+    MOI.set(model, MOA.Algorithm(), MOA.Lexicographic())
+    MOI.set(model, MOA.LexicographicAllPermutations(), false)
+    MOI.set(model, MOA.ObjectiveRelativeTolerance(1), 0.1)
+    MOI.set(model, MOI.Silent(), true)
+    x = MOI.add_variables(model, 4)
+    MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
+    MOI.add_constraint.(model, x, MOI.LessThan(1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
+    f = MOI.Utilities.operate(vcat, Float64, P * x...)
+    f.constants[4] = 1_000.0
+    MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
+    MOI.add_constraint(model, sum(1.0 * x[i] for i in 1:4), MOI.LessThan(2.0))
+    MOI.set(model, MOI.TimeLimitSec(), 0.0)
+    MOI.optimize!(model)
+    @test MOI.get(model, MOI.TerminationStatus()) == MOI.TIME_LIMIT
+    return
+end
+
 end
 
 TestLexicographic.run_tests()