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Bitshares and Steem don't need EOS, but Bitshares is looking at whether EOS tech could offer an upgrade to the current Graphene chain. The current Bitshares chain is capable of doing Visa/Mastercard (combined) tx volumes so there is a lot of headroom before an upgrade is needed. But, if EOS kicks ass, why not?

Not controlling your own blockchain could have serious cons. For example would bitshares be required to hold a sizable amount EOS to get the bandwidth they require?

EOS software is open source. I am thinking Bitshares could keep its same structure in terms of witnesses and have the those supporting the network switch over to the EOS software.... not necessarily running Bitshares on the main EOS blockchain (i.e., wouldn't even need EOS tokens in that scenario, to my knowledge)