Yes, but it's a very bad idea.
If this question is related to Access, you are working with a relational
database, not a spreadsheet. One of the really valuable things a relational
database allows you to do is avoid bad designs of that sort.
Without knowing more about your specific business and business rules, we can
only offer generalities, but it is possible to say that you need at least
two tables to accomplish this.
The first table is the one to which you are referring in this question.
Whatever it is for, it should have a Primary Key field, which uniquely
identifies each of the records in it. You can use that Primary Key to relate
or link this table to the second table, which is the one in which your
clients will be identified. You'll also have a client table, in which
attributes of your clients are stored.
Here's a quick look at the general structure of these tables:
tblClient
=============
ClientID (Primary Key, Autonumber)
ClientName
etc.
tblYourTable
=============
YourTablePimaryID (Primary Key, Autonumber)
FieldOne
etc.
tblClientsYourTable
============
ClientYourTableID (Primary Key, Autonumber)
ClientID (Foreign Key form tblClient)
YourTablePimaryID (Foreign Key from tblYourTable)
etc.
Note that the third table contains two Foreign Keys. One links to Clients
and the other links to your other table.
THis is typically referred to as a "Junction" table, and its purpose is to
handle requirements like the one you describe.
Here's a link to a Powerpoint presentation which discusses this sort of
relationship, and other aspects of table design.
http://www.gpcdata.com/downloads/saugpresentation.zip
George