Become more familiar with other 'second hand' information available other than the MSA.
If there is a One Engine Inoperative (OEI) escape route for the runway, fly it (with all engines of course) at best gradient performance. This should be well above the gradients allowed for in One Engine Inoperative operations.
If the aerodrome has a prescribed instrument approach, then there will be a Circling Minimum. Maintain Runway Track and best gradient of climb performance until reaching the Circling minimum. Turn Left or Right as appropriate to a downwind track, and stay within the Circling Area until reaching MSA minus 500 feet. It will be necessary for you to be familiar with the dimensions and prohibited sectors of the circling area. It will be necessary to establish Radio Nav and/or GPS fixes to ensure remaining within the area. By all means, use the highest performance category circling area, e.g. use Cat C or Cat D circling areas rather than 'your own'. Be sure to know, and allow for your turning radius.
If the airport has a runway aligned approach for landing in the opposite direction to your Takeoff, back track the ILS, VOR/DME, or NDB procedure, staying above the Glide Slope or restrictive steps. Your all engines gradient should be better than 5% (3°), and unless the approach gradient is significantly steeper than this, you have no problem.
If the airport has a DME arrival procedure, fly this in reverse, being careful to allow sufficient turn radius allowance for a turn-back if achieving a step is impossible.
If the holding fix is located within the circling area (common), stay in the circling area as earlier described until MHA minus 500 feet, and enter the holding pattern for further climb to MSA.
(PANS-OPS obstacle clearance requirements during departure climb are less than the standard 1000 feet allowed for in MSA or MHA, generally a little less than 400 feet. Using MSA and MHA minus 500 feet as the 'target' simplifies things somewhat).
There's a few ideas, they won't work in all cases, but will work in a great many. Obstacle clearance to MSA is a pilot responsibility, and full use should be made of all available information.
If in doubt, don't go.
Regards,
Old Smokey