Dear M.M.: Your chances may be better than you think. “It’s not at all unusual for entrepreneurs to start successful businesses while still working full-time,” notes Patrick McGinnis, a seasoned venture capitalist (and Harvard MBA) who wrote a book called The 10% Entrepreneur: Live Your Startup Dream Without Quitting Your Day Job. Especially since your startup is already profitable, he adds, “angels will at least be willing to hear you out, for a couple of good reasons.”

For one thing, a 2014 study from the University of Wisconsin at Madison that found that side businesses are 33% less likely to fail in their first five years than startups with full-time founders. The research also pointed out that 1 in 5 of the companies on Inc.’s annual list of the fastest-growing that year had been started by someone who, like you, was moonlighting.

That’s not surprising, partly because “when you leave a job to launch a business, the clock is ticking. You have only X amount of time before you run out of money,” says McGinnis. “By contrast, while you’re still living on a salary from your day job, you’re under a lot less pressure. It’s not ‘all or nothing’. So you tend to make calmer, better decisions, and that makes the business more sustainable in the long run.”

Most angels are aware of all that, and you’re unlikely to be the first part-time entrepreneur they’ve met with, McGinnis notes, so there’s no need to apologize for keeping your day job (at least for now). He suggests these three ways of raising the odds that you’ll get funded:

Build a team of talent. Ideally, at least one person should be working on the business full-time while you’re still part-time, especially since your plan is to speed up growth by buying out your main competitor. The 10% Entrepreneur describes how founders have expanded their startups by enlisting help. Peter Barlow, for instance, is an attorney who co-founded luxury car rental company Silvercar. He brought on two full-time partners — and raised $50 million from investors who included Facebook co-founder Eduardo Savarin — without ever quitting his day job at a law firm. At the very least, says McGinnis, “build a bench of talent around you. Invite people whose business acumen you admire to be on your advisory board. Recruit a talented former colleague who’s retired now to work X number of hours per week on the business. Investors want to see bench strength. The more awesome people you can surround yourself with, the less risky your venture looks.”

Write an excruciatingly detailed business plan. This is important for any entrepreneur who’s seeking funding, but particularly essential for you. “It needs to include a precise timetable for when you’ll be ready to start working on the business full-time,” says McGinnis. “You’ll also need specific projections for what will be happening in the meantime.” Since you’re hoping to use angels’ money to make an acquisition, spell out when that would happen, what you expect will be both the immediate and long-term effects on your customer base, revenues, and profits, and any related costs you might incur beyond the purchase price. Include individual bios of your team, with emphasis on the talent and experience they bring that are most relevant now. “This is one of those times,” notes McGinnis, “when there is no such thing as too much information.”

Be flexible. If a potential backer balks at your part-time status, McGinnis says, it might be at least in part because he or she isn’t convinced you’re eventually going to devote your full attention to the startup. “So be willing to set some unconventional terms,” he suggests. “For instance, you could offer to put some of the funding into an escrow account that you can only touch in 17 months, when you switch over to full time.” The more creative you’re willing to be in finding solutions to angels’ concerns, McGinnis adds, “the more likely it is that you’ll find not just an investor but a valuable ally and advisor as well.”

Good luck!

Talkback: If you’ve ever started a business in your spare time, did you find outside investors? How did you approach them? Leave a comment below.