JSFiddle - React, Tailwind, and code Playground

JavaScript

function intersection( arrs, limit ) {
    var result = [], posns = [];
    var j, v, next, n = arrs.length, count = 1;
    if( !n || limit <= 0 ) {
        return result; // nothing to do
    }
    if( n === 1 ) {
        // special case needed because main loop cannot handle this
        for( j = 0; j < arrs[0].length && result.length < limit; ++ j ) {
            v = arrs[0][j];
            if( v === v ) {
                result.push( v );
            }
        }
        return result;
    }
    for( j = 0; j < n; ++ j ) {
        if( !arrs[j].length ) {
            return result; // no intersection
        }
        posns[j] = 0;
    }
    next = arrs[n-1][0];
    ++ posns[n-1];
    while( true ) {
        for( j = 0; j < n; ++ j ) {
            do {
                if( posns[j] >= arrs[j].length ) {
                    return result; // ran out of values
                }
                v = arrs[j][posns[j]++];
            } while( v < next || v !== v );
            
            if( v !== next ) {
                count = 1;
                next = v;
            } else if( (++ count) >= n ) {
                result.push( next );
                if( result.length >= limit ) {
                    return result; // limit reached
                }
                if( posns[j] >= arrs[j].length ) {
                    return result; // ran out of values
                }
                next = arrs[j][posns[j]++];
                count = 1;
            }
        }
    }
}

function display( arrs, limit ) {
    var o = document.createElement( 'div' );
    o.innerText = '> ' + intersection(arrs,limit).join( ',' );
    document.body.appendChild( o );
}

display([[0, 3, 8, 11], [1, 3, 11, 15]], 0);
display([[0, 3, 8, 11], [1, 3, 11, 15]], 1);
display([[0, 3, 8, 11], [1, 3, 11, 15]], 2);
display([[0, 3, 8, 11], [1, 3, 11, 15]], 3);
display([[0, 3, 8, 11], [1, 3, 11, 15]], 8);
display([[0, 3, 8, 11], [1, 3, 11, 15]], 20);

display([[3,6,7,7,11], [3,6,7,7,11]],...