Here is a possible solution, starting with a query, that writes all distances in a single table first. The example uses OSM data imported with osm2pgrouting. Your attributes may have a different naming.
INSERT INTO data.distances SELECT 123456 AS source_id, a.*, b.id, b.the_geom FROM pgr_drivingDistance( 'SELECT gid AS id, source, target, cost_s AS cost, reverse_cost_s AS reverse_cost FROM osm.ways', 123456, 1000 ) AS a LEFT JOIN osm.ways_vertices_pgr AS b ON a.node = b.id; In the query above the source node ID is 123456, but you will run this query for each of your source nodes:
Then all your distances from each source node are stored in data.distances table and you can query the minimum distance to each node in your network:
SELECT DISTINCT ON (node) * FROM data.distances ORDER BY node, agg_cost ASC;