Pandigital Integers remaining Pandigital on Multiplication

Theorem
Certain pandigital integers remain pandigital when multiplying them by certain single-digit integers:

The sequence:
 * $1039675824, 1053826974, 1068253974, 1068379524, 1073968254, 1075396824, 1098765432, 1204756839, 1234567890, 1357802469$

contains all pandigital integers with at least $4$ nontrivial pandigital multiples, of which:


 * $1098765432, 1234567890$

has $5$.