Managing multiple LLC's with one "master" bank account?

[Johan Praats]

We're looking at PM software; one of the vendors suggested setting up a single "master" bank account into which all our tenants (regardless of which of my 10 LLC their property belongs to) pay their monthly rent. I would subsequently transfer the appropriate amounts into each LLC's bank account. Does this violate the spirit of a LLC, i.e. are we breaking that veil? The reason for this set-up is to avoid establishing 10 ACH accounts via my software vendor (set-up and monthly fees are high). thanks.