We investigate the constraints imposed by the first-year Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background (CMB) data extended to higher multipoles by data from ACBAR, BOOMERANG, CBI, and the VSA and by the large-scale structure data from the 2dF galaxy redshift survey on the possible amplitude of primordial isocurvature modes. A flat universe with cold dark matter (CDM) and cosmological constant Λ is assumed, and the baryon, CDM isocurvature (CI), and neutrino density (NID), and velocity (NIV) isocurvature modes are considered. Constraints on the allowed isocurvature contributions are established from the data for various combinations of the adiabatic mode and one, two, and three isocurvature modes, with intermode cross correlations allowed. Since baryon and CDM isocurvature are observationally virtually indistinguishable, these modes are not considered separately. We find that when just a single isocurvature mode is added, the present data allows an isocurvature fraction, in terms of the nonadiabatic contribution to the power in the CMB anisotropy, as large as 13±6, 7±4, and 13±7 percent for adiabatic plus the CI, NID, and NIV modes, respectively. When two isocurvature modes plus the adiabatic mode and cross correlations are allowed, these percentages rise to 47±16, 34±12, and 44±12 for the combinations CI+NID, CI+NIV, and NID+NIV, respectively. Finally, when all three isocurvature modes and cross correlations are allowed, the admissible isocurvature fraction rises to 57±9 percent. In our analysis we consider only scalar modes with a single common tilt parameter for all the modes and do not consider any possible primordial anisotropies in the local neutrino velocity distribution beyond quadrupole order. The sensitivity of the results to the choice of prior probability distribution is examined.