One of the SSIS package Scheduled job fails when two SSIS package jobs scheduled to run at same time

The application executes the SQL stored procedure to run the package and package executes as proxy account. We can schedule same package to run at same time with different variables or source files as input and when scheduled to run at same time, one package completes the execution and other package fails with below error. If there is some time gap then both packages succeeds.Can someone suggest how to fix the issue?

Started: 10:13:06 AM Error: 2018-05-21 10:13:06.78 Code: 0x00000001 Source: Script Task Description: Exception has been thrown by the target of an invocation. End Error DTExec: The package execution returned DTSER_FAILURE (1). Started: 10:13:06 AM Finished: 10:13:06 AM Elapsed: 0.795 seconds

Go through the second package and fix all the collisions/conflicts with the first package. Do they both try to lock the same table? Do they both use a temporary table with the same name? Any other things they have in common?