B737-800 Captain reported a NMAC with another aircraft during departure climbout. Flight crew took evasive action to avoid a collision.

Narrative

On departure ATC cleared us to 12;000 and assigned us a 050 heading. As we were climbing we received a TA; as I acquired the aircraft I realized it was going to result in a RA. I told the First Officer( we are going to have a RA; level out. or something to that effect) As he started to respond the RA began. I think it was initially a level out. I noticed that the other aircraft started to descend; and I think I verbalized that. We then got a descend RA. About that time the other aircraft turned towards us and started diving through our altitude towards us. It's hard to recollect what occurred but both the FO (First Officer) and I were 'in the fight' at that point to ensure he didn't hit us. we took aggressive maneuvering action to avoid a collision. We did get a bank angle warning; but no overspeed or under speed warnings. After avoiding the aircraft we returned to our heading and began the climb again. We advised ATC that we had multiple RA's and had to take evasive maneuvers. I think the vectoring from ATC; and the action of the other pilot turning towards us and dive through our altitude are the largest factors. One additional items that I am considering. The After Takeoff Flow in manual the trigger is 'after flap and slat retraction' during this event most of my time until the TA occurred was me waiting for the flaps to retract before beginning my after takeoff flow. I understand the rationale of wanting to ensure if the flaps fail to retract that is caught. I think more time available to scan for traffic is a higher importance. Suggestion: Better airspace management. On a side note. there was no support for the Flight Attendants. I had to personally walk the Flight Attendants down to the flight office; engage with their management. I also found it troubling that after a traumatic event for them the company was taking statements with out any representation besides myself. I'm not sure what the reason for taking statements while flight attendants were crying is; but it seemed like this was more focused on should they be payed for the trip removal then their fitness for duty. The flight attendants were expected to fly to ZZZ1 two hours after we landed until I got involved.