SFMC Support can change the value for the %%profile_center_url%% to whatever you want -- as @Kenneth mentioned.

I typically do this, which I outline here:

<a href='%%=MicrositeURL(888888,"subscriberMID", "12345678")=%%'>Update Profile</a>

Then in the profile center page:

<script type="text/javascript" runat="server">

    Platform.Load("core", "1.1.1");

    </script>
    %%[set @subscriberMID = RequestParameter("subscriberMID")]%%
    <script type="text/javascript" runat="server">

    if (Variable.GetValue("@subscriberMID") != "") {
        memberid = Variable.GetValue("@subscriberMID");
    } else {
        memberid = Attribute.GetValue("memberid");
    }

</script>

Same thing can be done with the CloudPagesURL() function.

Update

Here's my preferred way of doing this with the CloudPagesURL() function:

<a href='%%=redirectto(concat(CloudPagesURL(1234),"&mid=", memberid))=%%'>Preference Center</a>

Then in SSJS:

SetVar("mid", Request.GetQueryStringParameter("mid"));

function SetVar(varName, varValue){
    request[varName] = varValue ? varValue : "";
    Variable.SetValue(varName, varValue);
}

SFMC Support can change the value for the %%profile_center_url%% to whatever you want -- as @Kenneth mentioned.

I typically do this, which I outline here:

<a href='%%=MicrositeURL(888888,"subscriberMID", "12345678")=%%'>Update Profile</a>

Then in the profile center page:

<script type="text/javascript" runat="server">

    Platform.Load("core", "1.1.1");

    </script>
    %%[set @subscriberMID = RequestParameter("subscriberMID")]%%
    <script type="text/javascript" runat="server">

    if (Variable.GetValue("@subscriberMID") != "") {
        memberid = Variable.GetValue("@subscriberMID");
    } else {
        memberid = Attribute.GetValue("memberid");
    }

</script>

Same thing can be done with the CloudPagesURL() function.

Update

Since the CloudPagesURL() doesn't do URL parameters properly, here's my preferred way of doing this with the CloudPagesURL() function:

<a href='%%=redirectto(concat(CloudPagesURL(1234),"&mid=", memberid))=%%'>Preference Center</a>

Then in SSJS:

SetVar("mid", Request.GetQueryStringParameter("mid"));

function SetVar(varName, varValue){
    request[varName] = varValue ? varValue : "";
    Variable.SetValue(varName, varValue);
}

SFMC Support can change the value for the %%profile_center_url%% to whatever you want -- as @Kenneth mentioned.

I typically do this, which I outline here:

<a href='%%=MicrositeURL(888888,"subscriberMID", "12345678")=%%'>Update Profile</a>

Then in the profile center page:

<script type="text/javascript" runat="server">

    Platform.Load("core", "1.1.1");

    </script>
    %%[set @subscriberMID = RequestParameter("subscriberMID")]%%
    <script type="text/javascript" runat="server">

    if (Variable.GetValue("@subscriberMID") != "") {
        memberid = Variable.GetValue("@subscriberMID");
    } else {
        memberid = Attribute.GetValue("memberid");
    }

</script>

Same thing can be done with the CloudPagesURL() function.

SFMC Support can change the value for the %%profile_center_url%% to whatever you want -- as @Kenneth mentioned.

I typically do this, which I outline here:

<a href='%%=MicrositeURL(888888,"subscriberMID", "12345678")=%%'>Update Profile</a>

Then in the profile center page:

<script type="text/javascript" runat="server">

    Platform.Load("core", "1.1.1");

    </script>
    %%[set @subscriberMID = RequestParameter("subscriberMID")]%%
    <script type="text/javascript" runat="server">

    if (Variable.GetValue("@subscriberMID") != "") {
        memberid = Variable.GetValue("@subscriberMID");
    } else {
        memberid = Attribute.GetValue("memberid");
    }

</script>

Same thing can be done with the CloudPagesURL() function.

Update

Here's my preferred way of doing this with the CloudPagesURL() function:

<a href='%%=redirectto(concat(CloudPagesURL(1234),"&mid=", memberid))=%%'>Preference Center</a>

Then in SSJS:

SetVar("mid", Request.GetQueryStringParameter("mid"));

function SetVar(varName, varValue){
    request[varName] = varValue ? varValue : "";
    Variable.SetValue(varName, varValue);
}