diff --git a/check/TestHighsCDouble.cpp b/check/TestHighsCDouble.cpp
new file mode 100644
index 0000000000..2f17a40598
--- /dev/null
+++ b/check/TestHighsCDouble.cpp
@@ -0,0 +1,109 @@
+#include "HCheckConfig.h"
+#include "catch.hpp"
+#include "util/HighsCDouble.h"
+#include "util/HighsRandom.h"
+
+void testCeil(HighsCDouble x) {
+  double ceil_x;
+  double double_x;
+  ceil_x = double(ceil(x));
+  double_x = double(x);
+  REQUIRE(ceil_x >= double_x);
+  REQUIRE(ceil(x) >= x);
+}
+
+void testFloor(HighsCDouble x) {
+  double floor_x;
+  double double_x;
+  floor_x = double(floor(x));
+  double_x = double(x);
+  REQUIRE(floor_x <= double_x);
+  REQUIRE(floor(x) <= x);
+}
+
+TEST_CASE("HighsCDouble-ceil", "[util]") {
+  HighsCDouble x;
+  x = -1e-34;
+  testCeil(x);
+  x = -1e-32;
+  testCeil(x);
+  x = -1e-30;
+  testCeil(x);
+  x = -1e-23;
+  testCeil(x);
+  x = -1e-12;
+  testCeil(x);
+  x = -1e-1;
+  testCeil(x);
+  x = -0.99;
+  testCeil(x);
+
+  x = 0.99;
+  testCeil(x);
+  x = 1e-1;
+  testCeil(x);
+  x = 1e-12;
+  testCeil(x);
+  // This and rest failed in #2041
+  x = 1e-23;
+  testCeil(x);
+  x = 1e-30;
+  testCeil(x);
+  x = 1e-32;
+  testCeil(x);
+  x = 1e-34;
+  testCeil(x);
+
+  HighsRandom rand;
+  for (HighsInt k = 0; k < 1000; k++) {
+    double man = rand.fraction();
+    HighsInt power = 2 - rand.integer(5);
+    double exp = std::pow(10, power);
+    x = man * exp;
+    testCeil(x);
+  }
+}
+
+TEST_CASE("HighsCDouble-floor", "[util]") {
+  HighsCDouble x;
+
+  x = 1e-34;
+  testFloor(x);
+  x = 1e-32;
+  testFloor(x);
+  x = 1e-30;
+  testFloor(x);
+  x = 1e-23;
+  testFloor(x);
+  x = 1e-12;
+  testFloor(x);
+  x = 1e-1;
+  testFloor(x);
+  x = 0.99;
+  testFloor(x);
+
+  x = -0.99;
+  testFloor(x);
+  x = -1e-1;
+  testFloor(x);
+  x = -1e-12;
+  testFloor(x);
+  // This and rest failed in #2041
+  x = -1e-23;
+  testFloor(x);
+  x = -1e-30;
+  testFloor(x);
+  x = -1e-32;
+  testFloor(x);
+  x = -1e-34;
+  testFloor(x);
+
+  HighsRandom rand;
+  for (HighsInt k = 0; k < 1000; k++) {
+    double man = rand.fraction();
+    HighsInt power = 2 - rand.integer(5);
+    double exp = std::pow(10, power);
+    x = man * exp;
+    testFloor(x);
+  }
+}
diff --git a/check/TestMultiObjective.cpp b/check/TestMultiObjective.cpp
new file mode 100644
index 0000000000..013b8d3a8d
--- /dev/null
+++ b/check/TestMultiObjective.cpp
@@ -0,0 +1,56 @@
+#include "Highs.h"
+#include "catch.hpp"
+
+const bool dev_run = true;
+
+TEST_CASE("multi-objective", "[util]") {
+  HighsLp lp;
+  lp.num_col_ = 2;
+  lp.num_row_ = 3;
+  lp.col_cost_ = {0, 0};
+  lp.col_lower_ = {0, 0};
+  lp.col_upper_ = {kHighsInf, kHighsInf};
+  lp.row_lower_ = {-kHighsInf, -kHighsInf, -kHighsInf};
+  lp.row_upper_ = {18, 8, 14};
+  lp.a_matrix_.start_ = {0, 3, 6};
+  lp.a_matrix_.index_ = {0, 1, 2, 0, 1, 2};
+  lp.a_matrix_.value_ = {3, 1, 1, 1, 1, 2};
+  Highs h;
+  h.setOptionValue("output_flag", dev_run);
+  h.passModel(lp);
+
+  HighsLinearObjective linear_objective;
+  std::vector<HighsLinearObjective> linear_objectives;
+
+  // Begin with an illegal linear objective
+  linear_objective.weight = -1;
+  linear_objective.offset = -1;
+  linear_objective.coefficients = {2, 1, 0};
+  linear_objective.abs_tolerance = 0.0;
+  linear_objective.rel_tolerance = 1.0;
+  linear_objective.priority = 0;
+  REQUIRE(h.addLinearObjective(linear_objective) == HighsStatus::kError);
+
+  // Now legalise the linear objective so LP has nonunique optimal
+  // solutions on the line joining (2, 6) and (5, 3)
+  linear_objective.coefficients = {1, 1};
+  REQUIRE(h.addLinearObjective(linear_objective) == HighsStatus::kOk);
+
+  h.run();
+  h.writeSolution("", kSolutionStylePretty);
+  REQUIRE(h.getInfo().objective_function_value == -7);
+  // Save the linear objective for the next
+  linear_objectives.push_back(linear_objective);
+
+  // Add a second linear objective with a very small minimization
+  // weight that should push the optimal solution to (2, 6)
+  linear_objective.weight = 1e-4;
+  linear_objective.offset = 0;
+  linear_objective.coefficients = {-1, 0};
+  REQUIRE(h.addLinearObjective(linear_objective) == HighsStatus::kOk);
+
+  h.run();
+  h.writeSolution("", kSolutionStylePretty);
+  //  REQUIRE(h.getSolution().col_value[0] == 2);
+  //  REQUIRE(h.getSolution().col_value[1] == 6);
+}