My gut feel is I'd think twice before running a hard to drive design like mbl off any integrated amp if your goal is optimal performance and sound. I think you will pay a hefty premium to find one that can work really well versus separates. That's because very high build quality is needed to house a high power, high current amplifier in the same box as the pre-amp without being susceptible to higher noise levels and such. If a phono pre-amp were involved, the situation would be even tougher.
MBL speakers
I'm looking to simplify my setup and have currently MBL 116 with Rowlands Synergy 2i/501/PC1 monoblocks and MBL 1521/1511. If I were to keep the MBL 116 speakers can anyone recommend an integrated amp and one box player that would have similar quality to my setup. Please keep in mind that the speakers need to have quite a fair amount quality power to get the best. The Rowland have 500w and I had a Rowland Concentra II (150w) which really struggled to give its best. Thanks for looking!