It is but you will need to do it manually by modifying the associated custom search XML file that is created when you compile and save it.

To demonstrate create a new custom search form in Designer and place only a AnyText field and Submit button. Compile and save it as WLTST.

Close out Designer and navigate to the Laserfiche WebLink program directory (ie. C:\Program Files\Laserfiche\WebLink\Web Files\searchforms\YOURREPOSITORYNAME). In this directory you will see a file name WLTST.xml.

Open up the WLTST.XML file and you should see the following:

<?xml version="1.0" encoding="utf-8"?>
<Weblink.SearchForm xmlns:lf="http://schemas.laserfiche.com/Weblink/8/LfControls" xmlns:asp="http://schemas.laserfiche.com/Weblink/8/System.Web.UI.WebControls">
  <SearchForm Name="Multiple Text Box" Description="">
    <UI>
      <input runat="server" id="MultipleTextBox_Input0" resetval="" />
      <lf:Submit runat="server" id="MultipleTextBox_Button1" Text="Submit" />
    </UI>
    <Query>
      <And>
        <Constraint Type="Basic" Operator="eq" MatchAll="False" MatchWholeWord="True" UseWildcards="False" ControlID="MultipleTextBox_Input0" SearchName="AnyText" />
      </And>
    </Query>
    <SortOptions />
    <Summary>
    </Summary>
    <TokenMap>
      <Token Name="AnyText" ControlID="MultipleTextBox_Input0" />
    </TokenMap>
  </SearchForm>
</Weblink.SearchForm>

Basically you are going to make a copy of the "input" element and add another "Constraint" element for that newly copied "input" element.

<input runat="server" id="MultipleTextBox_Input0" resetval="" />

The important thing to remember is that your new input element needs to have a unique id:

<input runat="server" id="MultipleTextBox_Input1" resetval="" />

And your new constraint element must contain the new input element id:

<Constraint Type="Basic" Operator="eq" MatchAll="False" MatchWholeWord="True" UseWildcards="False" ControlID="MultipleTextBox_Input1" SearchName="AnyText" />

One thing I did change was the "<And>" element to "<Or>" since I wanted my search to find either values in the text boxes.

<Or>
   <Constraint Type="Basic" Operator="eq" MatchAll="False" MatchWholeWord="True" UseWildcards="False" ControlID="MultipleTextBox_Input0" SearchName="AnyText" />
   <Constraint Type="Basic" Operator="eq" MatchAll="False" MatchWholeWord="True" UseWildcards="False" ControlID="MultipleTextBox_Input1" SearchName="AnyText" />
</Or>

Below is the modified WLTST code:

<?xml version="1.0" encoding="utf-8"?>
<Weblink.SearchForm xmlns:lf="http://schemas.laserfiche.com/Weblink/8/LfControls" xmlns:asp="http://schemas.laserfiche.com/Weblink/8/System.Web.UI.WebControls">
  <SearchForm Name="Multiple Text Box" Description="">
    <UI>
      <input runat="server" id="MultipleTextBox_Input0" resetval="" />
      <input runat="server" id="MultipleTextbox_Input1" resetval=""/>
      <lf:Submit runat="server" id="MultipleTextBox_Button1" Text="Submit" />
    </UI>
    <Query>
      <Or>
        <Constraint Type="Basic" Operator="eq" MatchAll="False" MatchWholeWord="True" UseWildcards="False" ControlID="MultipleTextBox_Input0" SearchName="AnyText" />
      <Constraint Type="Basic" Operator="eq" MatchAll="False" MatchWholeWord="True" UseWildcards="False" ControlID="MultipleTextBox_Input1" SearchName="AnyText" />
      </Or>
    </Query>
    <SortOptions />
    <Summary>
    </Summary>
    <TokenMap>
      <Token Name="AnyText" ControlID="MultipleTextBox_Input0" />
    </TokenMap>
  </SearchForm>
</Weblink.SearchForm>

Save the file, close it, and then open up the search in WebLink. This was tested in WebLink 9 and worked as expected.

Hope this helps!